Package 'scoringutils'

Description

Adds a columns with relative skills computed by running pairwise comparisons on the scores. For more information on the computation of relative skill, see get_pairwise_comparisons(). Relative skill will be calculated for the aggregation level specified in by.

Usage

add_relative_skill(
  scores,
  by = "model",
  metric = intersect(c("wis", "crps", "brier_score"), names(scores)),
  baseline = NULL
)

Arguments

Description

Compute the absolute error of the median calculated as

$\textrm{abs}(\textrm{observed} - \textrm{median prediction})$

The median prediction is the predicted value for which quantile_level == 0.5, the function therefore requires 0.5 to be among the quantile levels in quantile_level.

Usage

ae_median_quantile(observed, predicted, quantile_level)

Arguments

Value

Numeric vector of length N with the absolute error of the median.

Input format

See Also

ae_median_sample()

Examples

observed <- rnorm(30, mean = 1:30)
predicted_values <- replicate(3, rnorm(30, mean = 1:30))
ae_median_quantile(
  observed, predicted_values, quantile_level = c(0.2, 0.5, 0.8)
)

Description

Absolute error of the median calculated as

$\textrm{abs}(\textrm{observevd} - \textrm{median\_prediction})$

Usage

ae_median_sample(observed, predicted)

Arguments

Value

vector with the scoring values

Input format

See Also

ae_median_quantile()

Examples

observed <- rnorm(30, mean = 1:30)
predicted_values <- matrix(rnorm(30, mean = 1:30))
ae_median_sample(observed, predicted_values)

Description

There are several “as_forecast_()⁠functions to process and validate a data.frame (or similar) or similar with forecasts and observations. If the input passes all input checks, those functions will be converted to a⁠forecast' object. A forecast object is a 'data.table' with a class 'forecast' and an additional class that depends on the forecast type. Every forecast type has its own 'as_forecast_()' function. See the details section below for more information on the expected input formats.

The ⁠as_forecast_<type>()⁠ functions give users some control over how their data is parsed. Using the arguments observed, predicted, model, etc. users can rename existing columns of their input data to match the required columns for a forecast object. Using the argument forecast_unit, users can specify the the columns that uniquely identify a single forecast (and remove the others, see set_forecast_unit() for details).

The following functions are available:

• as_forecast_point()

• as_forecast_binary()

• as_forecast_sample()

• as_forecast_quantile()

Arguments

Value

Depending on the forecast type, an object of the following class will be returned:

• forecast_binary for binary forecasts

• forecast_point for point forecasts

• forecast_sample for sample-based forecasts

• forecast_quantile for quantile-based forecasts

Forecast types and input formats

Various different forecast types / forecast formats are supported. At the moment, those are:

• point forecasts

• binary forecasts ("soft binary classification")

• nominal forecasts ("soft classification with multiple unordered classes")

• Probabilistic forecasts in a quantile-based format (a forecast is represented as a set of predictive quantiles)

• Probabilistic forecasts in a sample-based format (a forecast is represented as a set of predictive samples)

Forecast types are determined based on the columns present in the input data. Here is an overview of the required format for each forecast type:

All forecast types require a data.frame or similar with columns observed predicted, and model.

Point forecasts require a column observed of type numeric and a column predicted of type numeric.

Binary forecasts require a column observed of type factor with exactly two levels and a column predicted of type numeric with probabilities, corresponding to the probability that observed is equal to the second factor level. See details here for more information.

Nominal forecasts require a column observed of type factor with N levels, (where N is the number of possible outcomes), a column predicted of type numeric with probabilities (which sum to one across all possible outcomes), and a column predicted_label of type factor with N levels, denoting the outcome for which a probability is given. Forecasts must be complete, i.e. there must be a probability assigned to every possible outcome.

Quantile-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column quantile_level of type numeric with quantile-levels (between 0 and 1).

Sample-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column sample_id of type numeric with sample indices.

For more information see the vignettes and the example data (example_quantile, example_sample_continuous, example_sample_discrete, example_point(), example_binary, and example_nominal).

Forecast unit

In order to score forecasts, scoringutils needs to know which of the rows of the data belong together and jointly form a single forecasts. This is easy e.g. for point forecast, where there is one row per forecast. For quantile or sample-based forecasts, however, there are multiple rows that belong to a single forecast.

The forecast unit or unit of a single forecast is then described by the combination of columns that uniquely identify a single forecast. For example, we could have forecasts made by different models in various locations at different time points, each for several weeks into the future. The forecast unit could then be described as forecast_unit = c("model", "location", "forecast_date", "forecast_horizon"). scoringutils automatically tries to determine the unit of a single forecast. It uses all existing columns for this, which means that no columns must be present that are unrelated to the forecast unit. As a very simplistic example, if you had an additional row, "even", that is one if the row number is even and zero otherwise, then this would mess up scoring as scoringutils then thinks that this column was relevant in defining the forecast unit.

In order to avoid issues, we recommend setting the forecast unit explicitly, usually through the forecast_unit argument in the as_forecast() functions. This will drop unneeded columns, while making sure that all necessary, 'protected columns' like "predicted" or "observed" are retained.

See Also

Other functions to create forecast objects: as_forecast_binary(), as_forecast_nominal(), as_forecast_point(), as_forecast_quantile(), as_forecast_sample()

Examples

as_forecast_binary(example_binary)
as_forecast_quantile(
  example_quantile,
  forecast_unit = c("model", "target_type", "target_end_date",
                    "horizon", "location")
)

Description

Create a forecast object for binary forecasts. See more information on forecast types and expected input formats by calling ⁠?⁠as_forecast().

Usage

as_forecast_binary(
  data,
  forecast_unit = NULL,
  observed = NULL,
  predicted = NULL,
  model = NULL
)

Arguments

See Also

Other functions to create forecast objects: as_forecast, as_forecast_nominal(), as_forecast_point(), as_forecast_quantile(), as_forecast_sample()

Description

Common functionality for ⁠as_forecast_<type>⁠ functions

Usage

as_forecast_generic(
  data,
  forecast_unit = NULL,
  observed = NULL,
  predicted = NULL,
  model = NULL
)

Arguments

Details

This function splits out part of the functionality of ⁠as_forecast_<type>⁠ that is the same for all ⁠as_forecast_<type>⁠ functions. It renames the required columns, where appropriate, and sets the forecast unit.

Description

Nominal forecasts are a form of categorical forecasts where the possible outcomes that the observed values can assume are not ordered. In that sense, Nominal forecasts represent a generalisation of binary forecasts.

Usage

as_forecast_nominal(
  data,
  forecast_unit = NULL,
  observed = NULL,
  predicted = NULL,
  model = NULL,
  predicted_label = NULL
)

Arguments

See Also

Other functions to create forecast objects: as_forecast, as_forecast_binary(), as_forecast_point(), as_forecast_quantile(), as_forecast_sample()

Description

Create a forecast object for point forecasts. See more information on forecast types and expected input formats by calling ⁠?⁠as_forecast().

When converting a forecast_quantile object into a forecast_point object, the 0.5 quantile is extracted and returned as the point forecast.

Usage

as_forecast_point(data, ...)

## Default S3 method:
as_forecast_point(
  data,
  forecast_unit = NULL,
  observed = NULL,
  predicted = NULL,
  model = NULL,
  ...
)

## S3 method for class 'forecast_quantile'
as_forecast_point(data, ...)

Arguments

See Also

Other functions to create forecast objects: as_forecast, as_forecast_binary(), as_forecast_nominal(), as_forecast_quantile(), as_forecast_sample()

Description

Create a forecast object for quantile-based forecasts. See more information on forecast types and expected input formats by calling ⁠?⁠as_forecast().

When creating a forecast_quantile object from a forecast_sample object, the quantiles are estimated by computing empircal quantiles from the samples via quantile(). Note that empirical quantiles are a biased estimator for the true quantiles in particular in the tails of the distribution and when the number of available samples is low.

Usage

as_forecast_quantile(data, ...)

## Default S3 method:
as_forecast_quantile(
  data,
  forecast_unit = NULL,
  observed = NULL,
  predicted = NULL,
  model = NULL,
  quantile_level = NULL,
  ...
)

## S3 method for class 'forecast_sample'
as_forecast_quantile(
  data,
  probs = c(0.05, 0.25, 0.5, 0.75, 0.95),
  type = 7,
  ...
)

Arguments

See Also

Other functions to create forecast objects: as_forecast, as_forecast_binary(), as_forecast_nominal(), as_forecast_point(), as_forecast_sample()

Description

Create a forecast object for sample-based forecasts

Usage

as_forecast_sample(
  data,
  forecast_unit = NULL,
  observed = NULL,
  predicted = NULL,
  model = NULL,
  sample_id = NULL
)

Arguments

See Also

Other functions to create forecast objects: as_forecast, as_forecast_binary(), as_forecast_nominal(), as_forecast_point(), as_forecast_quantile()

Description

Function assesses whether input dimensions match. In the following, n is the number of observations / forecasts. Scalar values may be repeated to match the length of the other input. Allowed options are therefore:

• observed is vector of length 1 or length n

• predicted is:

  • a vector of of length 1 or length n

  • a matrix with n rows and 1 column

Usage

assert_dims_ok_point(observed, predicted)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Assert that an object is a forecast object (i.e. a data.table with a class forecast and an additional class ⁠forecast_*⁠ corresponding to the forecast type).

Usage

assert_forecast(forecast, forecast_type = NULL, verbose = TRUE, ...)

## Default S3 method:
assert_forecast(forecast, forecast_type = NULL, verbose = TRUE, ...)

## S3 method for class 'forecast_binary'
assert_forecast(forecast, forecast_type = NULL, verbose = TRUE, ...)

## S3 method for class 'forecast_point'
assert_forecast(forecast, forecast_type = NULL, verbose = TRUE, ...)

## S3 method for class 'forecast_quantile'
assert_forecast(forecast, forecast_type = NULL, verbose = TRUE, ...)

## S3 method for class 'forecast_sample'
assert_forecast(forecast, forecast_type = NULL, verbose = TRUE, ...)

Arguments

Value

Returns NULL invisibly.

Forecast types and input formats

Various different forecast types / forecast formats are supported. At the moment, those are:

• point forecasts

• binary forecasts ("soft binary classification")

• nominal forecasts ("soft classification with multiple unordered classes")

• Probabilistic forecasts in a quantile-based format (a forecast is represented as a set of predictive quantiles)

• Probabilistic forecasts in a sample-based format (a forecast is represented as a set of predictive samples)

Forecast types are determined based on the columns present in the input data. Here is an overview of the required format for each forecast type:

All forecast types require a data.frame or similar with columns observed predicted, and model.

Point forecasts require a column observed of type numeric and a column predicted of type numeric.

Binary forecasts require a column observed of type factor with exactly two levels and a column predicted of type numeric with probabilities, corresponding to the probability that observed is equal to the second factor level. See details here for more information.

Nominal forecasts require a column observed of type factor with N levels, (where N is the number of possible outcomes), a column predicted of type numeric with probabilities (which sum to one across all possible outcomes), and a column predicted_label of type factor with N levels, denoting the outcome for which a probability is given. Forecasts must be complete, i.e. there must be a probability assigned to every possible outcome.

Quantile-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column quantile_level of type numeric with quantile-levels (between 0 and 1).

Sample-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column sample_id of type numeric with sample indices.

For more information see the vignettes and the example data (example_quantile, example_sample_continuous, example_sample_discrete, example_point(), example_binary, and example_nominal).

Examples

forecast <- as_forecast_binary(example_binary)
assert_forecast(forecast)

Description

The function runs input checks that apply to all input data, regardless of forecast type. The function

• asserts that the forecast is a data.table which has columns observed and predicted, as well as a column called model.

• checks the forecast type and forecast unit

• checks there are no duplicate forecasts

• if appropriate, checks the number of samples / quantiles is the same for all forecasts.

Usage

assert_forecast_generic(data, verbose = TRUE)

Arguments

Value

returns the input

Description

Assert that forecast type is as expected

Usage

assert_forecast_type(data, actual = get_forecast_type(data), desired = NULL)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring binary forecasts.

Usage

assert_input_binary(observed, predicted)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring interval-based forecasts.

Usage

assert_input_interval(observed, lower, upper, interval_range)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring nominal forecasts.

Usage

assert_input_nominal(observed, predicted, predicted_label)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring point forecasts.

Usage

assert_input_point(observed, predicted)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring quantile-based forecasts.

Usage

assert_input_quantile(
  observed,
  predicted,
  quantile_level,
  unique_quantile_levels = TRUE
)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring sample-based forecasts.

Usage

assert_input_sample(observed, predicted)

Arguments

Value

Returns NULL invisibly if the assertion was successful and throws an error otherwise.

Description

Determines bias from quantile forecasts. For an increasing number of quantiles this measure converges against the sample based bias version for integer and continuous forecasts.

Usage

bias_quantile(observed, predicted, quantile_level, na.rm = TRUE)

Arguments

Details

For quantile forecasts, bias is measured as

$B_t = (1 - 2 \cdot \max \{i | q_{t,i} \in Q_t \land q_{t,i} \leq x_t\}) \mathbf{1}( x_t \leq q_{t, 0.5}) \\ + (1 - 2 \cdot \min \{i | q_{t,i} \in Q_t \land q_{t,i} \geq x_t\}) 1( x_t \geq q_{t, 0.5}),$

where $Q_t$ is the set of quantiles that form the predictive distribution at time $t$ and $x_t$ is the observed value. For consistency, we define $Q_t$ such that it always includes the element $q_{t, 0} = - \infty$ and $q_{t,1} = \infty$. $1()$ is the indicator function that is $1$ if the condition is satisfied and $0$ otherwise.

In clearer terms, bias $B_t$ is:

• $1 - 2 \cdot$ the maximum percentile rank for which the corresponding quantile is still smaller than or equal to the observed value, if the observed value is smaller than the median of the predictive distribution.

• $1 - 2 \cdot$ the minimum percentile rank for which the corresponding quantile is still larger than or equal to the observed value if the observed value is larger than the median of the predictive distribution..

• $0$ if the observed value is exactly the median (both terms cancel out)

Bias can assume values between -1 and 1 and is 0 ideally (i.e. unbiased).

Note that if the given quantiles do not contain the median, the median is imputed as the mean of the two innermost quantiles.

For a large enough number of quantiles, the percentile rank will equal the proportion of predictive samples below the observed value, and the bias metric coincides with the one for continuous forecasts (see bias_sample()).

Value

scalar with the quantile bias for a single quantile prediction

Input format

Examples

predicted <- matrix(c(1.5:23.5, 3.3:25.3), nrow = 2, byrow = TRUE)
quantile_level <- c(0.01, 0.025, seq(0.05, 0.95, 0.05), 0.975, 0.99)
observed <- c(15, 12.4)
bias_quantile(observed, predicted, quantile_level)

Description

Determines bias from predictive Monte-Carlo samples. The function automatically recognises whether forecasts are continuous or integer valued and adapts the Bias function accordingly.

Usage

bias_sample(observed, predicted)

Arguments

Details

For continuous forecasts, Bias is measured as

$B_t (P_t, x_t) = 1 - 2 * (P_t (x_t))$

where $P_t$ is the empirical cumulative distribution function of the prediction for the observed value $x_t$. Computationally, $P_t (x_t)$ is just calculated as the fraction of predictive samples for $x_t$ that are smaller than $x_t$.

For integer valued forecasts, Bias is measured as

$B_t (P_t, x_t) = 1 - (P_t (x_t) + P_t (x_t + 1))$

to adjust for the integer nature of the forecasts.

In both cases, Bias can assume values between -1 and 1 and is 0 ideally.

Value

Numeric vector of length n with the biases of the predictive samples with respect to the observed values.

Input format

References

The integer valued Bias function is discussed in Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15 Funk S, Camacho A, Kucharski AJ, Lowe R, Eggo RM, et al. (2019) Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15. PLOS Computational Biology 15(2): e1006785. doi:10.1371/journal.pcbi.1006785

Examples

## integer valued forecasts
observed <- rpois(30, lambda = 1:30)
predicted <- replicate(200, rpois(n = 30, lambda = 1:30))
bias_sample(observed, predicted)

## continuous forecasts
observed <- rnorm(30, mean = 1:30)
predicted <- replicate(200, rnorm(30, mean = 1:30))
bias_sample(observed, predicted)

Description

The functions loops over the column names and checks whether they are present. If an issue is encountered, the function immediately stops and returns a message with the first issue encountered.

Usage

check_columns_present(data, columns)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function assesses whether input dimensions match. In the following, n is the number of observations / forecasts. Scalar values may be repeated to match the length of the other input. Allowed options are therefore:

• observed is vector of length 1 or length n

• predicted is:

  • a vector of of length 1 or length n

  • a matrix with n rows and 1 column

Usage

check_dims_ok_point(observed, predicted)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Runs get_duplicate_forecasts() and returns a message if an issue is encountered

Usage

check_duplicates(data)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring binary forecasts.

Usage

check_input_binary(observed, predicted)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring interval-based forecasts.

Usage

check_input_interval(observed, lower, upper, interval_range)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring point forecasts.

Usage

check_input_point(observed, predicted)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring quantile-based forecasts.

Usage

check_input_quantile(observed, predicted, quantile_level)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function assesses whether the inputs correspond to the requirements for scoring sample-based forecasts.

Usage

check_input_sample(observed, predicted)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Function checks the number of quantiles or samples per forecast. If the number of quantiles or samples is the same for all forecasts, it returns TRUE and a string with an error message otherwise.

Usage

check_number_per_forecast(data, forecast_unit)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Helper function to check whether an input is a numeric vector.

Usage

check_numeric_vector(x, ...)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Tries to execute an expression. Internally, this is used to see whether assertions fail when checking inputs (i.e. to convert an ⁠assert_*()⁠ statement into a check). If the expression fails, the error message is returned. If the expression succeeds, TRUE is returned.

Usage

check_try(expr)

Arguments

Value

Returns TRUE if the check was successful and a string with an error message otherwise.

Description

Wrapper around the crps_sample() function from the scoringRules package. Can be used for continuous as well as integer valued forecasts

The Continuous ranked probability score (CRPS) can be interpreted as the sum of three components: overprediction, underprediction and dispersion. "Dispersion" is defined as the CRPS of the median forecast $m$. If an observation $y$ is greater than $m$ then overpredictoin is defined as the CRPS of the forecast for $y$ minus the dispersion component, and underprediction is zero. If, on the other hand, $y<m$ then underprediction is defined as the CRPS of the forecast for $y$ minus the dispersion component, and overprediction is zero.

The overprediction, underprediction and dispersion components correspond to those of the wis().

Usage

crps_sample(observed, predicted, separate_results = FALSE, ...)

dispersion_sample(observed, predicted, ...)

overprediction_sample(observed, predicted, ...)

underprediction_sample(observed, predicted, ...)

Arguments

Value

Vector with scores.

dispersion_sample(): a numeric vector with dispersion values (one per observation).

overprediction_quantile(): a numeric vector with overprediction values (one per observation).

underprediction_quantile(): a numeric vector with underprediction values (one per observation).

Input format

References

Alexander Jordan, Fabian Krüger, Sebastian Lerch, Evaluating Probabilistic Forecasts with scoringRules, https://www.jstatsoft.org/article/view/v090i12

Examples

observed <- rpois(30, lambda = 1:30)
predicted <- replicate(200, rpois(n = 30, lambda = 1:30))
crps_sample(observed, predicted)

Description

Wrapper around the dss_sample() function from the scoringRules package.

Usage

dss_sample(observed, predicted, ...)

Arguments

Value

Vector with scores.

Input format

References

Alexander Jordan, Fabian Krüger, Sebastian Lerch, Evaluating Probabilistic Forecasts with scoringRules, https://www.jstatsoft.org/article/view/v090i12

Examples

observed <- rpois(30, lambda = 1:30)
predicted <- replicate(200, rpois(n = 30, lambda = 1:30))
dss_sample(observed, predicted)

Description

Check whether the data.table has a column called model. If not, a column called model is added with the value ⁠Unspecified model⁠.

Usage

ensure_model_column(data)

Arguments

Value

The data.table with a column called model

Description

A data set with binary predictions for COVID-19 cases and deaths constructed from data submitted to the European Forecast Hub.

Usage

example_binary

Format

A data frame with the following columns:

location

the country for which a prediction was made

location_name

name of the country for which a prediction was made

target_end_date

the date for which a prediction was made

target_type

the target to be predicted (cases or deaths)

observed

A factor with observed values

forecast_date

the date on which a prediction was made

model

name of the model that generated the forecasts

horizon

forecast horizon in weeks

predicted

predicted value

Details

Predictions in the data set were constructed based on the continuous example data by looking at the number of samples below the mean prediction. The outcome was constructed as whether or not the actually observed value was below or above that mean prediction. This should not be understood as sound statistical practice, but rather as a practical way to create an example data set.

The data was created using the script create-example-data.R in the inst/ folder (or the top level folder in a compiled package).

Source

https://github.com/european-modelling-hubs/covid19-forecast-hub-europe/commit/a42867b1ea152c57e25b04f9faa26cfd4bfd8fa6/

Description

A data set with predictions for COVID-19 cases and deaths submitted to the European Forecast Hub.

Usage

example_nominal

Format

A data frame with the following columns:

location

the country for which a prediction was made

target_end_date

the date for which a prediction was made

target_type

the target to be predicted (cases or deaths)

observed

Numeric: observed values

location_name

name of the country for which a prediction was made

forecast_date

the date on which a prediction was made

predicted_label

outcome that a probabilty corresponds to

predicted

predicted value

model

name of the model that generated the forecasts

horizon

forecast horizon in weeks

Details

The data was created using the script create-example-data.R in the inst/ folder (or the top level folder in a compiled package).

Source

https://github.com/european-modelling-hubs/covid19-forecast-hub-europe/commit/a42867b1ea152c57e25b04f9faa26cfd4bfd8fa6/

Description

A data set with predictions for COVID-19 cases and deaths submitted to the European Forecast Hub. This data set is like the quantile example data, only that the median has been replaced by a point forecast.

Usage

example_point

Format

A data frame with the following columns:

location

the country for which a prediction was made

target_end_date

the date for which a prediction was made

target_type

the target to be predicted (cases or deaths)

observed

observed values

location_name

name of the country for which a prediction was made

forecast_date

the date on which a prediction was made

predicted

predicted value

model

name of the model that generated the forecasts

horizon

forecast horizon in weeks

Details

The data was created using the script create-example-data.R in the inst/ folder (or the top level folder in a compiled package).

Source

https://github.com/european-modelling-hubs/covid19-forecast-hub-europe/commit/a42867b1ea152c57e25b04f9faa26cfd4bfd8fa6/

Description

A data set with predictions for COVID-19 cases and deaths submitted to the European Forecast Hub.

Usage

example_quantile

Format

A data frame with the following columns:

location

the country for which a prediction was made

target_end_date

the date for which a prediction was made

target_type

the target to be predicted (cases or deaths)

observed

Numeric: observed values

location_name

name of the country for which a prediction was made

forecast_date

the date on which a prediction was made

quantile_level

quantile level of the corresponding prediction

predicted

predicted value

model

name of the model that generated the forecasts

horizon

forecast horizon in weeks

Details

The data was created using the script create-example-data.R in the inst/ folder (or the top level folder in a compiled package).

Source

https://github.com/european-modelling-hubs/covid19-forecast-hub-europe/commit/a42867b1ea152c57e25b04f9faa26cfd4bfd8fa6/

Description

A data set with continuous predictions for COVID-19 cases and deaths constructed from data submitted to the European Forecast Hub.

Usage

example_sample_continuous

Format

A data frame with the following columns:

location

the country for which a prediction was made

target_end_date

the date for which a prediction was made

target_type

the target to be predicted (cases or deaths)

observed

observed values

location_name

name of the country for which a prediction was made

forecast_date

the date on which a prediction was made

model

name of the model that generated the forecasts

horizon

forecast horizon in weeks

predicted

predicted value

sample_id

id for the corresponding sample

Details

The data was created using the script create-example-data.R in the inst/ folder (or the top level folder in a compiled package).

Source

https://github.com/european-modelling-hubs/covid19-forecast-hub-europe/commit/a42867b1ea152c57e25b04f9faa26cfd4bfd8fa6/

Description

A data set with integer predictions for COVID-19 cases and deaths constructed from data submitted to the European Forecast Hub.

Usage

example_sample_discrete

Format

A data frame with the following columns:

location

the country for which a prediction was made

target_end_date

the date for which a prediction was made

target_type

the target to be predicted (cases or deaths)

observed

observed values

location_name

name of the country for which a prediction was made

forecast_date

the date on which a prediction was made

model

name of the model that generated the forecasts

horizon

forecast horizon in weeks

predicted

predicted value

sample_id

id for the corresponding sample

Details

The data was created using the script create-example-data.R in the inst/ folder (or the top level folder in a compiled package).

Source

https://github.com/european-modelling-hubs/covid19-forecast-hub-europe/commit/a42867b1ea152c57e25b04f9faa26cfd4bfd8fa6/

Description

Calculate the correlation between different metrics for a data.frame of scores as produced by score().

Usage

get_correlations(scores, metrics = get_metrics(scores), ...)

Arguments

Value

An object of class scores (a data.table with an additional attribute metrics holding the names of the scores) with correlations between different metrics

Examples

library(magrittr) # pipe operator

scores <- example_quantile %>%
 as_forecast_quantile() %>%
 score()

get_correlations(scores)

Description

For a validated forecast object in a quantile-based format (see as_forecast() for more information), this function computes:

• interval coverage of central prediction intervals

• quantile coverage for predictive quantiles

• the deviation between desired and actual coverage (both for interval and quantile coverage)

Coverage values are computed for a specific level of grouping, as specified in the by argument. By default, coverage values are computed per model.

Interval coverage

Interval coverage for a given interval range is defined as the proportion of observations that fall within the corresponding central prediction intervals. Central prediction intervals are symmetric around the median and formed by two quantiles that denote the lower and upper bound. For example, the 50% central prediction interval is the interval between the 0.25 and 0.75 quantiles of the predictive distribution.

Quantile coverage

Quantile coverage for a given quantile level is defined as the proportion of observed values that are smaller than the corresponding predictive quantile. For example, the 0.5 quantile coverage is the proportion of observed values that are smaller than the 0.5 quantile of the predictive distribution. Just as above, for a single observation and the quantile of a single predictive distribution, the value will either be TRUE or FALSE.

Coverage deviation

The coverage deviation is the difference between the desired coverage (can be either interval or quantile coverage) and the actual coverage. For example, if the desired coverage is 90% and the actual coverage is 80%, the coverage deviation is -0.1.

Usage

get_coverage(forecast, by = "model")

Arguments

Value

A data.table with columns as specified in by and additional columns for the coverage values described above

a data.table with columns "interval_coverage", "interval_coverage_deviation", "quantile_coverage", "quantile_coverage_deviation" and the columns specified in by.

Examples

library(magrittr) # pipe operator
example_quantile %>%
  as_forecast_quantile() %>%
  get_coverage(by = "model")

Description

Helper function to identify duplicate forecasts, i.e. instances where there is more than one forecast for the same prediction target.

Usage

get_duplicate_forecasts(data, counts = FALSE)

Arguments

Value

A data.frame with all rows for which a duplicate forecast was found

Examples

example <- rbind(example_quantile, example_quantile[1000:1010])
get_duplicate_forecasts(example)

Description

Given a data set with forecasts, this function counts the number of available forecasts. The level of grouping can be specified using the by argument (e.g. to count the number of forecasts per model, or the number of forecasts per model and location). This is useful to determine whether there are any missing forecasts.

Usage

get_forecast_counts(
  forecast,
  by = get_forecast_unit(forecast),
  collapse = c("quantile_level", "sample_id")
)

Arguments

Value

A data.table with columns as specified in by and an additional column "count" with the number of forecasts.

Examples

library(magrittr) # pipe operator
example_quantile %>%
  as_forecast_quantile() %>%
  get_forecast_counts(by = c("model", "target_type"))

Description

Helper function to infer the forecast type based on a data.frame or similar with forecasts and observed values. See the details section below for information on the different forecast types.

Usage

get_forecast_type(data)

Arguments

Value

Character vector of length one with either "binary", "quantile", "sample" or "point".

Forecast types and input formats

Various different forecast types / forecast formats are supported. At the moment, those are:

• point forecasts

• binary forecasts ("soft binary classification")

• nominal forecasts ("soft classification with multiple unordered classes")

• Probabilistic forecasts in a quantile-based format (a forecast is represented as a set of predictive quantiles)

• Probabilistic forecasts in a sample-based format (a forecast is represented as a set of predictive samples)

Forecast types are determined based on the columns present in the input data. Here is an overview of the required format for each forecast type:

All forecast types require a data.frame or similar with columns observed predicted, and model.

Point forecasts require a column observed of type numeric and a column predicted of type numeric.

Binary forecasts require a column observed of type factor with exactly two levels and a column predicted of type numeric with probabilities, corresponding to the probability that observed is equal to the second factor level. See details here for more information.

Nominal forecasts require a column observed of type factor with N levels, (where N is the number of possible outcomes), a column predicted of type numeric with probabilities (which sum to one across all possible outcomes), and a column predicted_label of type factor with N levels, denoting the outcome for which a probability is given. Forecasts must be complete, i.e. there must be a probability assigned to every possible outcome.

Quantile-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column quantile_level of type numeric with quantile-levels (between 0 and 1).

Sample-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column sample_id of type numeric with sample indices.

For more information see the vignettes and the example data (example_quantile, example_sample_continuous, example_sample_discrete, example_point(), example_binary, and example_nominal).

Description

Helper function to get the unit of a single forecast, i.e. the column names that define where a single forecast was made for. This just takes all columns that are available in the data and subtracts the columns that are protected, i.e. those returned by get_protected_columns() as well as the names of the metrics that were specified during scoring, if any.

Usage

get_forecast_unit(data)

Arguments

Value

A character vector with the column names that define the unit of a single forecast

Forecast unit

In order to score forecasts, scoringutils needs to know which of the rows of the data belong together and jointly form a single forecasts. This is easy e.g. for point forecast, where there is one row per forecast. For quantile or sample-based forecasts, however, there are multiple rows that belong to a single forecast.

The forecast unit or unit of a single forecast is then described by the combination of columns that uniquely identify a single forecast. For example, we could have forecasts made by different models in various locations at different time points, each for several weeks into the future. The forecast unit could then be described as forecast_unit = c("model", "location", "forecast_date", "forecast_horizon"). scoringutils automatically tries to determine the unit of a single forecast. It uses all existing columns for this, which means that no columns must be present that are unrelated to the forecast unit. As a very simplistic example, if you had an additional row, "even", that is one if the row number is even and zero otherwise, then this would mess up scoring as scoringutils then thinks that this column was relevant in defining the forecast unit.

In order to avoid issues, we recommend setting the forecast unit explicitly, usually through the forecast_unit argument in the as_forecast() functions. This will drop unneeded columns, while making sure that all necessary, 'protected columns' like "predicted" or "observed" are retained.

Description

When applying a scoring rule via score(), the names of the scoring rules become column names of the resulting data.table. In addition, an attribute metrics will be added to the output, holding the names of the scores as a vector.

This is done so that functions like get_forecast_unit() or summarise_scores() can still identify which columns are part of the forecast unit and which hold a score.

get_metrics() accesses and returns the metrics attribute. If there is no attribute, the function will return NULL (or, if error = TRUE will produce an error instead). In addition, it checks the column names of the input for consistency with the data stored in the metrics attribute.

Handling a missing or inconsistent metrics attribute:

If the metrics attribute is missing or is not consistent with the column names of the data.table, you can either

• run score() again, specifying names for the scoring rules manually, or

• add/update the attribute manually using attr(scores, "metrics") <- c("names", "of", "your", "scores") (the order does not matter).

Usage

get_metrics(scores, error = FALSE)

Arguments

Value

Character vector with the names of the scoring rules that were used for scoring or NULL if no scores were computed previously.

Description

Compare scores obtained by different models in a pairwise tournament. All combinations of two models are compared against each other based on the overlapping set of available forecasts common to both models.

The input should be a scores object as produced by score(). Note that adding additional unrelated columns can unpredictably change results, as all present columns are taken into account when determining the set of overlapping forecasts between two models.

The output of the pairwise comparisons is a set of mean score ratios, relative skill scores and p-values.

The following illustrates the pairwise comparison process:

Mean score ratios

For every pair of two models, a mean score ratio is computed. This is simply the mean score of the first model divided by the mean score of the second. Mean score ratios are computed based on the set of overlapping forecasts between the two models. That means that only scores for those targets are taken into account for which both models have submitted a forecast.

(Scaled) Relative skill scores

The relative score of a model is the geometric mean of all mean score ratios which involve that model. If a baseline is provided, scaled relative skill scores will be calculated as well. Scaled relative skill scores are simply the relative skill score of a model divided by the relative skill score of the baseline model.

p-values

In addition, the function computes p-values for the comparison between two models (again based on the set of overlapping forecasts). P-values can be computed in two ways: based on a nonparametric Wilcoxon signed-rank test (internally using wilcox.test() with paired = TRUE) or based on a permutation test. The permutation test is based on the difference in mean scores between two models. The default null hypothesis is that the mean score difference is zero (see permutation_test()). Adjusted p-values are computed by calling p.adjust() on the raw p-values.

The code for the pairwise comparisons is inspired by an implementation by Johannes Bracher. The implementation of the permutation test follows the function permutationTest from the surveillance package by Michael Höhle, Andrea Riebler and Michaela Paul.

Usage

get_pairwise_comparisons(
  scores,
  by = "model",
  metric = intersect(c("wis", "crps", "brier_score"), names(scores)),
  baseline = NULL,
  ...
)

Arguments

Value

A data.table with the results of pairwise comparisons containing the mean score ratios (mean_scores_ratio), unadjusted (pval) and adjusted (adj_pval) p-values, and relative skill values of each model (..._relative_skill). If a baseline model is given then the scaled relative skill is reported as well (..._scaled_relative_skill).

Author(s)

Nikos Bosse [email protected]

Johannes Bracher, [email protected]

Examples

library(magrittr) # pipe operator

scores <- example_quantile %>%
 as_forecast_quantile() %>%
 score()

pairwise <- get_pairwise_comparisons(scores, by = "target_type")
pairwise2 <- get_pairwise_comparisons(
  scores, by = "target_type", baseline = "EuroCOVIDhub-baseline"
)

library(ggplot2)
plot_pairwise_comparisons(pairwise, type = "mean_scores_ratio") +
  facet_wrap(~target_type)

Description

Compute the Probability Integral Transformation (PIT) for validated forecast objects.

Usage

get_pit(forecast, by, n_replicates = 100)

Arguments

Value

A data.table with PIT values according to the grouping specified in by.

References

Sebastian Funk, Anton Camacho, Adam J. Kucharski, Rachel Lowe, Rosalind M. Eggo, W. John Edmunds (2019) Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15, doi:10.1371/journal.pcbi.1006785

Examples

example <- as_forecast_sample(example_sample_continuous)
result <- get_pit(example, by = "model")
plot_pit(result)

# example with quantile data
example <- as_forecast_quantile(example_quantile)
result <- get_pit(example, by = "model")
plot_pit(result)

Description

Internal helper function to get the type of a vector (usually of observed or predicted values). The function checks whether the input is a factor, or else whether it is integer (or can be coerced to integer) or whether it's continuous.

Usage

get_type(x)

Arguments

Value

Character vector of length one with either "classification", "integer", or "continuous".

Description

Check whether the observed value is within a given central prediction interval. The prediction interval is defined by a lower and an upper bound formed by a pair of predictive quantiles. For example, a 50% prediction interval is formed by the 0.25 and 0.75 quantiles of the predictive distribution.

Usage

interval_coverage(observed, predicted, quantile_level, interval_range = 50)

Arguments

Value

A vector of length n with elements either TRUE, if the observed value is within the corresponding prediction interval, and FALSE otherwise.

Input format

Examples

observed <- c(1, -15, 22)
predicted <- rbind(
  c(-1, 0, 1, 2, 3),
  c(-2, 1, 2, 2, 4),
   c(-2, 0, 3, 3, 4)
)
quantile_level <- c(0.1, 0.25, 0.5, 0.75, 0.9)
interval_coverage(observed, predicted, quantile_level)

Description

Check the agreement between desired and actual interval coverage of a forecast.

The function is similar to interval_coverage(), but takes all provided prediction intervals into account and compares nominal interval coverage (i.e. the desired interval coverage) with the actual observed interval coverage.

A central symmetric prediction interval is defined by a lower and an upper bound formed by a pair of predictive quantiles. For example, a 50% prediction interval is formed by the 0.25 and 0.75 quantiles of the predictive distribution. Ideally, a forecaster should aim to cover about 50% of all observed values with their 50% prediction intervals, 90% of all observed values with their 90% prediction intervals, and so on.

For every prediction interval, the deviation is computed as the difference between the observed interval coverage and the nominal interval coverage For a single observed value and a single prediction interval, coverage is always either 0 or 1 (FALSE or TRUE). This is not the case for a single observed value and multiple prediction intervals, but it still doesn't make that much sense to compare nominal (desired) coverage and actual coverage for a single observation. In that sense coverage deviation only really starts to make sense as a metric when averaged across multiple observations).

Positive values of interval coverage deviation are an indication for underconfidence, i.e. the forecaster could likely have issued a narrower forecast. Negative values are an indication for overconfidence, i.e. the forecasts were too narrow.

$\textrm{interval coverage deviation} = \mathbf{1}(\textrm{observed value falls within interval}) - \textrm{nominal interval coverage}$

The interval coverage deviation is then averaged across all prediction intervals. The median is ignored when computing coverage deviation.

Usage

interval_coverage_deviation(observed, predicted, quantile_level)

Arguments

Value

A numeric vector of length n with the interval coverage deviation for each forecast (with the forecast itself comprising one or multiple prediction intervals).

Input format

Examples

observed <- c(1, -15, 22)
predicted <- rbind(
  c(-1, 0, 1, 2, 3),
  c(-2, 1, 2, 2, 4),
  c(-2, 0, 3, 3, 4)
)
quantile_level <- c(0.1, 0.25, 0.5, 0.75, 0.9)
interval_coverage_deviation(observed, predicted, quantile_level)

Description

Proper Scoring Rule to score quantile predictions, following Gneiting and Raftery (2007). Smaller values are better.

The score is computed as

$\textrm{score} = (\textrm{upper} - \textrm{lower}) + \frac{2}{\alpha}(\textrm{lower} - \textrm{observed}) * \mathbf{1}(\textrm{observed} < \textrm{lower}) + \frac{2}{\alpha}(\textrm{observed} - \textrm{upper}) * \mathbf{1}(\textrm{observed} > \textrm{upper})$

where $\mathbf{1}()$ is the indicator function and indicates how much is outside the prediction interval. $\alpha$ is the decimal value that indicates how much is outside the prediction interval.

To improve usability, the user is asked to provide an interval range in percentage terms, i.e. interval_range = 90 (percent) for a 90 percent prediction interval. Correspondingly, the user would have to provide the 5% and 95% quantiles (the corresponding alpha would then be 0.1). No specific distribution is assumed, but the interval has to be symmetric around the median (i.e you can't use the 0.1 quantile as the lower bound and the 0.7 quantile as the upper bound). Non-symmetric quantiles can be scored using the function quantile_score().

Usage

interval_score(
  observed,
  lower,
  upper,
  interval_range,
  weigh = TRUE,
  separate_results = FALSE
)

Arguments

Value

Vector with the scoring values, or a list with separate entries if separate_results is TRUE.

References

Strictly Proper Scoring Rules, Prediction,and Estimation, Tilmann Gneiting and Adrian E. Raftery, 2007, Journal of the American Statistical Association, Volume 102, 2007 - Issue 477

Evaluating epidemic forecasts in an interval format, Johannes Bracher, Evan L. Ray, Tilmann Gneiting and Nicholas G. Reich, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008618 # nolint

Examples

observed <- rnorm(30, mean = 1:30)
interval_range <- rep(90, 30)
alpha <- (100 - interval_range) / 100
lower <- qnorm(alpha / 2, rnorm(30, mean = 1:30))
upper <- qnorm((1 - alpha / 2), rnorm(30, mean = 11:40))

scoringutils:::interval_score(
  observed = observed,
  lower = lower,
  upper = upper,
  interval_range = interval_range
)

# gives a warning, as the interval_range should likely be 50 instead of 0.5
scoringutils:::interval_score(
  observed = 4, upper = 8, lower = 2, interval_range = 0.5
)

# example with missing values and separate results
scoringutils:::interval_score(
  observed = c(observed, NA),
  lower = c(lower, NA),
  upper = c(NA, upper),
  separate_results = TRUE,
  interval_range = 90
)

Description

Test whether an object is a forecast object (see as_forecast() for more information).

You can test for a specific ⁠forecast_*⁠ class using the appropriate ⁠is_forecast_*⁠ function.

Usage

is_forecast(x)

is_forecast_sample(x)

is_forecast_binary(x)

is_forecast_point(x)

is_forecast_quantile(x)

is_forecast_nominal(x)

Arguments

Value

is_forecast: TRUE if the object is of class forecast, FALSE otherwise.

⁠is_forecast_<type>*⁠: TRUE if the object is of class ⁠forecast_*⁠ in addition to class forecast, FALSE otherwise.

Examples

forecast_binary <- as_forecast_binary(example_binary)
is_forecast(forecast_binary)

Description

Function that shifts a value by some offset and then applies the natural logarithm to it.

Usage

log_shift(x, offset = 0, base = exp(1))

Arguments

Details

The output is computed as log(x + offset)

Value

A numeric vector with transformed values

References

Transformation of forecasts for evaluating predictive performance in an epidemiological context Nikos I. Bosse, Sam Abbott, Anne Cori, Edwin van Leeuwen, Johannes Bracher, Sebastian Funk medRxiv 2023.01.23.23284722 doi:10.1101/2023.01.23.23284722 https://www.medrxiv.org/content/10.1101/2023.01.23.23284722v1 # nolint

Examples

library(magrittr) # pipe operator
log_shift(1:10)
log_shift(0:9, offset = 1)

example_quantile[observed > 0, ] %>%
  as_forecast_quantile() %>%
  transform_forecasts(fun = log_shift, offset = 1)

Description

Log score for nominal outcomes

The Log Score is the negative logarithm of the probability assigned to the observed value. It is a proper scoring rule. Small values are better (best is zero, worst is infinity).

Usage

logs_nominal(observed, predicted, predicted_label)

Arguments

Value

A numeric vector of size n with log scores

Examples

factor_levels <- c("one", "two", "three")
predicted_label <- factor(c("one", "two", "three"), levels = factor_levels)
observed <- factor(c("one", "three", "two"), levels = factor_levels)
predicted <- matrix(c(0.8, 0.1, 0.4,
                      0.1, 0.2, 0.4,
                      0.1, 0.7, 0.2),
                    nrow = 3)
logs_nominal(observed, predicted, predicted_label)

Description

This function is a wrapper around the logs_sample() function from the scoringRules package.

The function should be used to score continuous predictions only. While the Log Score is in theory also applicable to discrete forecasts, the problem lies in the implementation: The Log score needs a kernel density estimation, which is not well defined with integer-valued Monte Carlo Samples. The Log score can be used for specific discrete probability distributions. See the scoringRules package for more details.

Usage

logs_sample(observed, predicted, ...)

Arguments

Value

Vector with scores.

Input format

References

Alexander Jordan, Fabian Krüger, Sebastian Lerch, Evaluating Probabilistic Forecasts with scoringRules, https://www.jstatsoft.org/article/view/v090i12

Examples

observed <- rpois(30, lambda = 1:30)
predicted <- replicate(200, rpois(n = 30, lambda = 1:30))
logs_sample(observed, predicted)

Description

Sharpness is the ability of the model to generate predictions within a narrow range and dispersion is the lack thereof. It is a data-independent measure, and is purely a feature of the forecasts themselves.

Dispersion of predictive samples corresponding to one single observed value is measured as the normalised median of the absolute deviation from the median of the predictive samples. For details, see mad() and the explanations given in Funk et al. (2019)

Usage

mad_sample(observed = NULL, predicted, ...)

Arguments

Value

Vector with dispersion values.

Input format

References

Funk S, Camacho A, Kucharski AJ, Lowe R, Eggo RM, Edmunds WJ (2019) Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15. PLoS Comput Biol 15(2): e1006785. doi:10.1371/journal.pcbi.1006785

Examples

predicted <- replicate(200, rpois(n = 30, lambda = 1:30))
mad_sample(predicted = predicted)

Description

Helper function that returns a named list of default scoring rules suitable for binary forecasts.

The default scoring rules are:

• "brier_score" = brier_score()

• "log_score" = logs_binary()

Usage

metrics_binary(select = NULL, exclude = NULL)

Arguments

Value

A list of scoring functions.

Input format

Examples

metrics_binary()
metrics_binary(select = "brier_score")
metrics_binary(exclude = "log_score")

Description

Helper function that returns a named list of default scoring rules suitable for nominal forecasts.

The default scoring rules are:

• "log_score" = logs_nominal()

Usage

metrics_nominal(select = NULL, exclude = NULL)

Arguments

Value

A list of scoring functions.

Examples

metrics_nominal()
metrics_nominal(select = "log_score")

Description

Helper function that returns a named list of default scoring rules suitable for point forecasts.

The default scoring rules are:

• "ae_point" = ae()

• "se_point" = se()

• "ape" = ape()

Usage

metrics_point(select = NULL, exclude = NULL)

Arguments

Value

A list of scoring functions.

Input format

Examples

metrics_point()
metrics_point(select = "ape")

Description

Helper function that returns a named list of default scoring rules suitable for forecasts in a quantile-based format.

The default scoring rules are:

• "wis" = wis

• "overprediction" = overprediction_quantile()

• "underprediction" = underprediction_quantile()

• "dispersion" = dispersion_quantile()

• "bias" = bias_quantile()

• "interval_coverage_50" = interval_coverage()

• "interval_coverage_90" = purrr::partial( interval_coverage, interval_range = 90 )

• "interval_coverage_deviation" = interval_coverage_deviation(),

• "ae_median" = ae_median_quantile()

Note: The interval_coverage_90 scoring rule is created by modifying interval_coverage(), making use of the function purrr::partial(). This construct allows the function to deal with arbitrary arguments in ..., while making sure that only those that interval_coverage() can accept get passed on to it. interval_range = 90 is set in the function definition, as passing an argument interval_range = 90 to score() would mean it would also get passed to interval_coverage_50.

Usage

metrics_quantile(select = NULL, exclude = NULL)

Arguments

Value

A list of scoring functions.

Input format

Examples

metrics_quantile()
metrics_quantile(select = "wis")

Description

Helper function that returns a named list of default scoring rules suitable for forecasts in a sample-based format.

The default scoring rules are:

• "crps" = crps_sample()

• "overprediction" = overprediction_sample()

• "underprediction" = underprediction_sample()

• "dispersion" = dispersion_sample()

• "log_score" = logs_sample()

• "dss" = dss_sample()

• "mad" = mad_sample()

• "bias" = bias_sample()

• "ae_median" = ae_median_sample()

• "se_mean" = se_mean_sample()

Usage

metrics_sample(select = NULL, exclude = NULL)

Arguments

Value

A list of scoring functions.

Input format

Examples

metrics_sample()
metrics_sample(select = "mad")

Description

Uses a Probability integral transformation (PIT) (or a randomised PIT for integer forecasts) to assess the calibration of predictive Monte Carlo samples.

Usage

pit_sample(observed, predicted, n_replicates = 100)

Arguments

Details

Calibration or reliability of forecasts is the ability of a model to correctly identify its own uncertainty in making predictions. In a model with perfect calibration, the observed data at each time point look as if they came from the predictive probability distribution at that time.

Equivalently, one can inspect the probability integral transform of the predictive distribution at time t,

$u_t = F_t (x_t)$

where $x_t$ is the observed data point at time $t \textrm{ in } t_1, …, t_n$, n being the number of forecasts, and $F_t$ is the (continuous) predictive cumulative probability distribution at time t. If the true probability distribution of outcomes at time t is $G_t$ then the forecasts $F_t$ are said to be ideal if $F_t = G_t$ at all times t. In that case, the probabilities $u_t$ are distributed uniformly.

In the case of discrete outcomes such as incidence counts, the PIT is no longer uniform even when forecasts are ideal. In that case a randomised PIT can be used instead:

$u_t = P_t(k_t) + v * (P_t(k_t) - P_t(k_t - 1) )$

where $k_t$ is the observed count, $P_t(x)$ is the predictive cumulative probability of observing incidence k at time t, $P_t (-1) = 0$ by definition and v is standard uniform and independent of k. If $P_t$ is the true cumulative probability distribution, then $u_t$ is standard uniform.

The function checks whether integer or continuous forecasts were provided. It then applies the (randomised) probability integral and tests the values $u_t$ for uniformity using the Anderson-Darling test.

As a rule of thumb, there is no evidence to suggest a forecasting model is miscalibrated if the p-value found was greater than a threshold of p >= 0.1, some evidence that it was miscalibrated if 0.01 < p < 0.1, and good evidence that it was miscalibrated if p <= 0.01. However, the AD-p-values may be overly strict and there actual usefulness may be questionable. In this context it should be noted, though, that uniformity of the PIT is a necessary but not sufficient condition of calibration.

Value

A vector with PIT-values. For continuous forecasts, the vector will correspond to the length of observed. For integer forecasts, a randomised PIT will be returned of length length(observed) * n_replicates.

References

Sebastian Funk, Anton Camacho, Adam J. Kucharski, Rachel Lowe, Rosalind M. Eggo, W. John Edmunds (2019) Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15, doi:10.1371/journal.pcbi.1006785

See Also

get_pit()

Examples

## continuous predictions
observed <- rnorm(20, mean = 1:20)
predicted <- replicate(100, rnorm(n = 20, mean = 1:20))
pit <- pit_sample(observed, predicted)
plot_pit(pit)

## integer predictions
observed <- rpois(20, lambda = 1:20)
predicted <- replicate(100, rpois(n = 20, lambda = 1:20))
pit <- pit_sample(observed, predicted, n_replicates = 30)
plot_pit(pit)

Description

Plots a heatmap of correlations between different metrics.

Usage

plot_correlations(correlations, digits = NULL)

Arguments

Value

A ggplot object showing a coloured matrix of correlations between metrics.

A ggplot object with a visualisation of correlations between metrics

Examples

library(magrittr) # pipe operator
scores <- example_quantile %>%
  as_forecast_quantile %>%
  score()
correlations <- scores %>%
  summarise_scores() %>%
  get_correlations()
plot_correlations(correlations, digits = 2)

Description

Visualise Where Forecasts Are Available.

Usage

plot_forecast_counts(
  forecast_counts,
  x,
  y = "model",
  x_as_factor = TRUE,
  show_counts = TRUE
)

Arguments

Value

A ggplot object with a plot of forecast counts

Examples

library(ggplot2)
library(magrittr) # pipe operator
forecast_counts <- example_quantile %>%
  as_forecast_quantile %>%
  get_forecast_counts(by = c("model", "target_type", "target_end_date"))
plot_forecast_counts(
 forecast_counts, x = "target_end_date", show_counts = FALSE
) +
 facet_wrap("target_type")

Description

This function can be used to create a heatmap of one metric across different groups, e.g. the interval score obtained by several forecasting models in different locations.

Usage

plot_heatmap(scores, y = "model", x, metric)

Arguments

Value

A ggplot object showing a heatmap of the desired metric

Examples

library(magrittr) # pipe operator
scores <- example_quantile %>%
  as_forecast_quantile %>%
  score()
scores <- summarise_scores(scores, by = c("model", "target_type"))
scores <- summarise_scores(
  scores, by = c("model", "target_type"),
  fun = signif, digits = 2
)

plot_heatmap(scores, x = "target_type", metric = "bias")

Description

Plot interval coverage values (see get_coverage() for more information).

Usage

plot_interval_coverage(coverage, colour = "model")

Arguments

Value

ggplot object with a plot of interval coverage

Examples

example <- as_forecast_quantile(example_quantile)
coverage <- get_coverage(example, by = "model")
plot_interval_coverage(coverage)

Description

Creates a heatmap of the ratios or pvalues from a pairwise comparison between models.

Usage

plot_pairwise_comparisons(
  comparison_result,
  type = c("mean_scores_ratio", "pval")
)

Arguments

Value

A ggplot object with a heatmap of mean score ratios from pairwise comparisons.

Examples

library(ggplot2)
library(magrittr) # pipe operator
scores <- example_quantile %>%
  as_forecast_quantile %>%
  score()
pairwise <- get_pairwise_comparisons(scores, by = "target_type")
plot_pairwise_comparisons(pairwise, type = "mean_scores_ratio") +
  facet_wrap(~target_type)

Description

Make a simple histogram of the probability integral transformed values to visually check whether a uniform distribution seems likely.

Usage

plot_pit(pit, num_bins = "auto", breaks = NULL)

Arguments

Value

A ggplot object with a histogram of PIT values

Examples

library(magrittr) # pipe operator

# PIT histogram in vector based format
observed <- rnorm(30, mean = 1:30)
predicted <- replicate(200, rnorm(n = 30, mean = 1:30))
pit <- pit_sample(observed, predicted)
plot_pit(pit)

# quantile-based pit
pit <- example_quantile %>%
  as_forecast_quantile() %>%
  get_pit(by = "model")
plot_pit(pit, breaks = seq(0.1, 1, 0.1))

# sample-based pit
pit <- example_sample_discrete %>%
  as_forecast_sample %>%
  get_pit(by = "model")
plot_pit(pit)

Description

Plot quantile coverage values (see get_coverage() for more information).

Usage

plot_quantile_coverage(coverage, colour = "model")

Arguments

Value

A ggplot object with a plot of interval coverage

Examples

example <- as_forecast_quantile(example_quantile)
coverage <- get_coverage(example, by = "model")
plot_quantile_coverage(coverage)

Description

Visualise the components of the weighted interval score: penalties for over-prediction, under-prediction and for high dispersion (lack of sharpness).

Usage

plot_wis(scores, x = "model", relative_contributions = FALSE, flip = FALSE)

Arguments

Value

A ggplot object showing a contributions from the three components of the weighted interval score.

A ggplot object with a visualisation of the WIS decomposition

References

Bracher J, Ray E, Gneiting T, Reich, N (2020) Evaluating epidemic forecasts in an interval format. https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008618

Examples

library(ggplot2)
library(magrittr) # pipe operator
scores <- example_quantile %>%
  as_forecast_quantile %>%
  score()
scores <- summarise_scores(scores, by = c("model", "target_type"))

plot_wis(scores,
  x = "model",
  relative_contributions = TRUE
) +
  facet_wrap(~target_type)
plot_wis(scores,
  x = "model",
  relative_contributions = FALSE
) +
  facet_wrap(~target_type, scales = "free_x")

Description

This function prints information about a forecast object, including "Forecast type", "Score columns", "Forecast unit".

Usage

## S3 method for class 'forecast'
print(x, ...)

Arguments

Value

Returns x invisibly.

Examples

dat <- as_forecast_quantile(example_quantile)
print(dat)

Description

Proper Scoring Rule to score quantile predictions. Smaller values are better. The quantile score is closely related to the interval score (see wis()) and is the quantile equivalent that works with single quantiles instead of central prediction intervals.

The quantile score, also called pinball loss, for a single quantile level $\tau$ is defined as

$\text{QS}_\tau(F, y) = 2 \cdot \{ \mathbf{1}(y \leq q_\tau) - \tau\} \cdot (q_\tau - y) = \begin{cases} 2 \cdot (1 - \tau) * q_\tau - y, & \text{if } y \leq q_\tau\\ 2 \cdot \tau * |q_\tau - y|, & \text{if } y > q_\tau, \end{cases}$

with $q_\tau$ being the $\tau$-quantile of the predictive distribution $F$, and $\mathbf{1}(\cdot)$ the indicator function.

The weighted interval score for a single prediction interval can be obtained as the average of the quantile scores for the lower and upper quantile of that prediction interval:

$\text{WIS}_\alpha(F, y) = \frac{\text{QS}_{\alpha/2}(F, y) + \text{QS}_{1 - \alpha/2}(F, y)}{2}.$

See the SI of Bracher et al. (2021) for more details.

quantile_score() returns the average quantile score across the quantile levels provided. For a set of quantile levels that form pairwise central prediction intervals, the quantile score is equivalent to the interval score.

Usage

quantile_score(observed, predicted, quantile_level, weigh = TRUE)

Arguments

Value

Numeric vector of length n with the quantile score. The scores are averaged across quantile levels if multiple quantile levels are provided (the result of calling rowMeans() on the matrix of quantile scores that is computed based on the observed and predicted values).

Input format

References

Strictly Proper Scoring Rules, Prediction,and Estimation, Tilmann Gneiting and Adrian E. Raftery, 2007, Journal of the American Statistical Association, Volume 102, 2007 - Issue 477

Evaluating epidemic forecasts in an interval format, Johannes Bracher, Evan L. Ray, Tilmann Gneiting and Nicholas G. Reich, 2021, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008618

Examples

observed <- rnorm(10, mean = 1:10)
alpha <- 0.5

lower <- qnorm(alpha / 2, observed)
upper <- qnorm((1 - alpha / 2), observed)

qs_lower <- quantile_score(observed,
  predicted = matrix(lower),
  quantile_level = alpha / 2
)
qs_upper <- quantile_score(observed,
  predicted = matrix(upper),
  quantile_level = 1 - alpha / 2
)
interval_score <- (qs_lower + qs_upper) / 2
interval_score2 <- quantile_score(
  observed,
  predicted = cbind(lower, upper),
  quantile_level = c(alpha / 2, 1 - alpha / 2)
)

# this is the same as the following
wis(
  observed,
  predicted = cbind(lower, upper),
  quantile_level = c(alpha / 2, 1 - alpha / 2)
)

Description

score() applies a selection of scoring metrics to a forecast object (a data.table with forecasts and observations) (see as_forecast()). score() is a generic that dispatches to different methods depending on the class of the input data.

See the Forecast types and input formats section for more information on forecast types and input formats. For additional help and examples, check out the Getting Started Vignette as well as the paper Evaluating Forecasts with scoringutils in R.

Usage

score(forecast, metrics, ...)

## S3 method for class 'forecast_binary'
score(forecast, metrics = metrics_binary(), ...)

## S3 method for class 'forecast_nominal'
score(forecast, metrics = metrics_nominal(), ...)

## S3 method for class 'forecast_point'
score(forecast, metrics = metrics_point(), ...)

## S3 method for class 'forecast_sample'
score(forecast, metrics = metrics_sample(), ...)

## S3 method for class 'forecast_quantile'
score(forecast, metrics = metrics_quantile(), ...)

Arguments

Details

Customising metrics

If you want to pass arguments to a scoring function, you need change the scoring function itself via e.g. purrr::partial() and pass an updated list of functions with your custom metric to the metrics argument in score(). For example, to use interval_coverage() with interval_range = 90, you would define a new function, e.g. interval_coverage_90 <- purrr::partial(interval_coverage, interval_range = 90) and pass this new function to metrics in score().

Note that if you want to pass a variable as an argument, you can unquote it with ⁠!!⁠ to make sure the value is evaluated only once when the function is created. Consider the following example:

custom_arg <- "foo"
print1 <- purrr::partial(print, x = custom_arg)
print2 <- purrr::partial(print, x = !!custom_arg)

custom_arg <- "bar"
print1() # prints 'bar'
print2() # prints 'foo'

Value

An object of class scores. This object is a data.table with unsummarised scores (one score per forecast) and has an additional attribute metrics with the names of the metrics used for scoring. See summarise_scores()) for information on how to summarise scores.

Forecast types and input formats

Various different forecast types / forecast formats are supported. At the moment, those are:

• point forecasts

• binary forecasts ("soft binary classification")

• nominal forecasts ("soft classification with multiple unordered classes")

• Probabilistic forecasts in a quantile-based format (a forecast is represented as a set of predictive quantiles)

• Probabilistic forecasts in a sample-based format (a forecast is represented as a set of predictive samples)

Forecast types are determined based on the columns present in the input data. Here is an overview of the required format for each forecast type:

All forecast types require a data.frame or similar with columns observed predicted, and model.

Point forecasts require a column observed of type numeric and a column predicted of type numeric.

Binary forecasts require a column observed of type factor with exactly two levels and a column predicted of type numeric with probabilities, corresponding to the probability that observed is equal to the second factor level. See details here for more information.

Nominal forecasts require a column observed of type factor with N levels, (where N is the number of possible outcomes), a column predicted of type numeric with probabilities (which sum to one across all possible outcomes), and a column predicted_label of type factor with N levels, denoting the outcome for which a probability is given. Forecasts must be complete, i.e. there must be a probability assigned to every possible outcome.

Quantile-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column quantile_level of type numeric with quantile-levels (between 0 and 1).

Sample-based forecasts require a column observed of type numeric, a column predicted of type numeric, and a column sample_id of type numeric with sample indices.

For more information see the vignettes and the example data (example_quantile, example_sample_continuous, example_sample_discrete, example_point(), example_binary, and example_nominal).

Forecast unit

In order to score forecasts, scoringutils needs to know which of the rows of the data belong together and jointly form a single forecasts. This is easy e.g. for point forecast, where there is one row per forecast. For quantile or sample-based forecasts, however, there are multiple rows that belong to a single forecast.

The forecast unit or unit of a single forecast is then described by the combination of columns that uniquely identify a single forecast. For example, we could have forecasts made by different models in various locations at different time points, each for several weeks into the future. The forecast unit could then be described as forecast_unit = c("model", "location", "forecast_date", "forecast_horizon"). scoringutils automatically tries to determine the unit of a single forecast. It uses all existing columns for this, which means that no columns must be present that are unrelated to the forecast unit. As a very simplistic example, if you had an additional row, "even", that is one if the row number is even and zero otherwise, then this would mess up scoring as scoringutils then thinks that this column was relevant in defining the forecast unit.

In order to avoid issues, we recommend setting the forecast unit explicitly, usually through the forecast_unit argument in the as_forecast() functions. This will drop unneeded columns, while making sure that all necessary, 'protected columns' like "predicted" or "observed" are retained.

Author(s)

Nikos Bosse [email protected]

References

Bosse NI, Gruson H, Cori A, van Leeuwen E, Funk S, Abbott S (2022) Evaluating Forecasts with scoringutils in R. doi:10.48550/arXiv.2205.07090

Examples

library(magrittr) # pipe operator


validated <- as_forecast_quantile(example_quantile)
score(validated) %>%
  summarise_scores(by = c("model", "target_type"))

# set forecast unit manually (to avoid issues with scoringutils trying to
# determine the forecast unit automatically)
example_quantile %>%
  as_forecast_quantile(
    forecast_unit = c(
      "location", "target_end_date", "target_type", "horizon", "model"
    )
  ) %>%
  score()

# forecast formats with different metrics
## Not run: 
score(as_forecast_binary(example_binary))
score(as_forecast_quantile(example_quantile))
score(as_forecast_point(example_point))
score(as_forecast_sample(example_sample_discrete))
score(as_forecast_sample(example_sample_continuous))

## End(Not run)

Description

Brier score

The Brier Score is the mean squared error between the probabilistic prediction and the observed outcome. The Brier score is a proper scoring rule. Small values are better (best is 0, the worst is 1).

$\textrm{Brier\_Score} = (\textrm{prediction} - \textrm{outcome})^2,$

where $\textrm{outcome} \in \{0, 1\}$, and $\textrm{prediction} \in [0, 1]$ represents the probability that the outcome is equal to 1.

Log score for binary outcomes

The Log Score is the negative logarithm of the probability assigned to the observed value. It is a proper scoring rule. Small values are better (best is zero, worst is infinity).

Usage

brier_score(observed, predicted)

logs_binary(observed, predicted)

Arguments

Details

The functions require users to provide observed values as a factor in order to distinguish its input from the input format required for scoring point forecasts. Internally, however, factors will be converted to numeric values. A factor ⁠observed = factor(c(0, 1, 1, 0, 1)⁠ with two levels (0 and 1) would internally be coerced to a numeric vector (in this case this would result in the numeric vector c(1, 2, 2, 1, 1)). After subtracting 1, the resulting vector (c(0, 1, 1, 0) in this case) is used for internal calculations. All predictions are assumed represent the probability that the outcome is equal of the last/highest factor level (in this case that the outcome is equal to 1).

You could alternatively also provide a vector like observed = factor(c("a", "b", "b", "a")) (with two levels, a and b), which would result in exactly the same internal representation. Probabilities then represent the probability that the outcome is equal to "b". If you want your predictions to be probabilities that the outcome is "a", then you could of course make observed a factor with levels swapped, i.e. observed = factor(c("a", "b", "b", "a"), levels = c("b", "a"))

Value

A numeric vector of size n with the Brier scores

A numeric vector of size n with log scores

Input format

Examples

observed <- factor(sample(c(0, 1), size = 30, replace = TRUE))
predicted <- runif(n = 30, min = 0, max = 1)

brier_score(observed, predicted)
logs_binary(observed, predicted)

Description

Squared error of the mean calculated as

$\textrm{mean}(\textrm{observed} - \textrm{mean prediction})^2$

The mean prediction is calculated as the mean of the predictive samples.

Usage

se_mean_sample(observed, predicted)

Arguments

Input format

Examples

observed <- rnorm(30, mean = 1:30)
predicted_values <- matrix(rnorm(30, mean = 1:30))
se_mean_sample(observed, predicted_values)

Description

Helper function to return only the scoring rules selected by the user from a list of possible functions.

Usage

select_metrics(metrics, select = NULL, exclude = NULL)

Arguments

Value

A list of scoring functions.

Examples

select_metrics(
  metrics = metrics_binary(),
  select = "brier_score"
)
select_metrics(
  metrics = metrics_binary(),
  exclude = "log_score"
)

Description

Helper function to set the unit of a single forecast (i.e. the combination of columns that uniquely define a single forecast) manually. This simple function keeps the columns specified in forecast_unit (plus additional protected columns, e.g. for observed values, predictions or quantile levels) and removes duplicate rows. set_forecast_unit() will mainly be called when constructing a forecast object (see as_forecast()) via the forecast_unit argument there.

If not done explicitly, scoringutils attempts to determine the unit of a single forecast automatically by simply assuming that all column names are relevant to determine the forecast unit. This may lead to unexpected behaviour, so setting the forecast unit explicitly can help make the code easier to debug and easier to read.

Usage

set_forecast_unit(data, forecast_unit)

Arguments

Value

A data.table with only those columns kept that are relevant to scoring or denote the unit of a single forecast as specified by the user.

Examples

library(magrittr) # pipe operator
example_quantile %>%
  set_forecast_unit(
    c("location", "target_end_date", "target_type", "horizon", "model")
  )

Summarise scores as produced by score()

Description

Summarise scores as produced by score().

summarise_scores relies on a way to identify the names of the scores and distinguish them from columns that denote the unit of a single forecast. Internally, this is done via a stored attribute, metrics that stores the names of the scores. This means, however, that you need to be careful with renaming scores after they have been produced by score(). If you do, you also have to manually update the attribute by calling attr(scores, "metrics") <- new_names.

Usage

summarise_scores(scores, by = "model", fun = mean, ...)

summarize_scores(scores, by = "model", fun = mean, ...)

Arguments

Value

A data.table with summarised scores. Scores are summarised according to the names of the columns of the original data specified in by using the fun passed to summarise_scores().

Examples

library(magrittr) # pipe operator
scores <- example_sample_continuous %>%
 as_forecast_sample() %>%
 score()

# get scores by model
summarise_scores(scores, by = "model")

# get scores by model and target type
summarise_scores(scores, by = c("model", "target_type"))

# get standard deviation
summarise_scores(scores, by = "model", fun = sd)

# round digits
summarise_scores(scores,by = "model") %>%
  summarise_scores(fun = signif, digits = 2)

Description

The function checks whether all column names are NOT present. If none of the columns are present, the function returns TRUE. If one or more columns are present, the function returns FALSE.

Usage

test_columns_not_present(data, columns)

Arguments

Value

Returns TRUE if none of the columns are present and FALSE otherwise

Description

The function checks whether all column names are present. If one or more columns are missing, the function returns FALSE. If all columns are present, the function returns TRUE.

Usage

test_columns_present(data, columns)

Arguments

Value

Returns TRUE if all columns are present and FALSE otherwise

Description

Checks type of the necessary columns.

Usage

test_forecast_type_is_binary(data)

Arguments

Value

Returns TRUE if basic requirements are satisfied and FALSE otherwise

Description

Checks type of the necessary columns.

Usage

test_forecast_type_is_nominal(data)

Arguments

Value

Returns TRUE if basic requirements are satisfied and FALSE otherwise

Description

Checks type of the necessary columns.

Usage

test_forecast_type_is_point(data)

Arguments

Value

Returns TRUE if basic requirements are satisfied and FALSE otherwise

Description

Checks type of the necessary columns.

Usage

test_forecast_type_is_quantile(data)

Arguments

Value

Returns TRUE if basic requirements are satisfied and FALSE otherwise

Description

Checks type of the necessary columns.

Usage

test_forecast_type_is_sample(data)

Arguments

Value

Returns TRUE if basic requirements are satisfied and FALSE otherwise

Description

A theme for ggplot2 plots used in scoringutils.

Usage

theme_scoringutils()

Value

A ggplot2 theme

Description

Function to transform forecasts and observed values before scoring.

Usage

transform_forecasts(
  forecast,
  fun = log_shift,
  append = TRUE,
  label = "log",
  ...
)

Arguments

Details

There are a few reasons, depending on the circumstances, for why this might be desirable (check out the linked reference for more info). In epidemiology, for example, it may be useful to log-transform incidence counts before evaluating forecasts using scores such as the weighted interval score (WIS) or the continuous ranked probability score (CRPS). Log-transforming forecasts and observations changes the interpretation of the score from a measure of absolute distance between forecast and observation to a score that evaluates a forecast of the exponential growth rate. Another motivation can be to apply a variance-stabilising transformation or to standardise incidence counts by population.

Note that if you want to apply a transformation, it is important to transform the forecasts and observations and then apply the score. Applying a transformation after the score risks losing propriety of the proper scoring rule.

Value

A forecast object with either a transformed version of the data, or one with both the untransformed and the transformed data. includes the original data as well as a transformation of the original data. There will be one additional column, ‘scale’, present which will be set to "natural" for the untransformed forecasts.

Author(s)

Nikos Bosse [email protected]

References

Transformation of forecasts for evaluating predictive performance in an epidemiological context Nikos I. Bosse, Sam Abbott, Anne Cori, Edwin van Leeuwen, Johannes Bracher, Sebastian Funk medRxiv 2023.01.23.23284722 doi:10.1101/2023.01.23.23284722 https://www.medrxiv.org/content/10.1101/2023.01.23.23284722v1

Examples

library(magrittr) # pipe operator

# transform forecasts using the natural logarithm
# negative values need to be handled (here by replacing them with 0)
example_quantile %>%
  .[, observed := ifelse(observed < 0, 0, observed)] %>%
  as_forecast_quantile() %>%
# Here we use the default function log_shift() which is essentially the same
# as log(), but has an additional arguments (offset) that allows you add an
# offset before applying the logarithm.
  transform_forecasts(append = FALSE) %>%
  head()

# alternatively, integrating the truncation in the transformation function:
example_quantile %>%
  as_forecast_quantile() %>%
 transform_forecasts(
   fun = function(x) {log_shift(pmax(0, x))}, append = FALSE
 ) %>%
 head()

# specifying an offset for the log transformation removes the
# warning caused by zeros in the data
example_quantile %>%
  as_forecast_quantile() %>%
  .[, observed := ifelse(observed < 0, 0, observed)] %>%
  transform_forecasts(offset = 1, append = FALSE) %>%
  head()

# adding square root transformed forecasts to the original ones
example_quantile %>%
  .[, observed := ifelse(observed < 0, 0, observed)] %>%
  as_forecast_quantile() %>%
  transform_forecasts(fun = sqrt, label = "sqrt") %>%
  score() %>%
  summarise_scores(by = c("model", "scale"))

# adding multiple transformations
example_quantile %>%
  as_forecast_quantile() %>%
  .[, observed := ifelse(observed < 0, 0, observed)] %>%
  transform_forecasts(fun = log_shift, offset = 1) %>%
  transform_forecasts(fun = sqrt, label = "sqrt") %>%
  head()

Description

The function re-validates an existing forecast object. It is similar to assert_forecast(), but returns the input data instead of an invisible NULL. See as_forecast() for details on the expected input formats.

Usage

validate_forecast(forecast, forecast_type = NULL, verbose = TRUE)

Arguments

Value

Returns NULL invisibly.

Examples

forecast <- as_forecast_binary(example_binary)
assert_forecast(forecast)

Description

This function validates whether the list of metrics is a list of valid functions.

The function is used in score() to make sure that all metrics are valid functions.

Usage

validate_metrics(metrics)

Arguments

Value

A named list of metrics, with those filtered out that are not valid functions

Description

The WIS is a proper scoring rule used to evaluate forecasts in an interval- / quantile-based format. See Bracher et al. (2021). Smaller values are better.

As the name suggest the score assumes that a forecast comes in the form of one or multiple central prediction intervals. A prediction interval is characterised by a lower and an upper bound formed by a pair of predictive quantiles. For example, a 50% central prediction interval is formed by the 0.25 and 0.75 quantiles of the predictive distribution.