Simulation setup | Fitting a constant and a random-walk model | Weekly estimates from per-case draws | Estimates one week after the last onset | Estimates six weeks after the last onset | Other settings | Interpreting the two estimates

The problem | A line list | Preparing the data at a cut-off | Fitting | Covariates and time-varying CFR | Delay family and fixing the delay | Recovery timing | Caveats

Why stratify, and why pool | A six-site line list | Three fits: complete, no, and partial pooling | Reading the estimates | Shrinkage | Varying the delay by group | Check the fit

What delay distributions represent | Specifying delays | Why naive discretisation is biased | How primarycensored corrects this | Composing multiple delays | Truncation | Fitting delay distributions from data | References

Set up | Data | Parameters | Delays: incubation period and reporting delay | Generation time | Initial reproduction number | Running the model | Default options | Reducing the accuracy of the approximate Gaussian Process | Adjusting for future susceptible depletion | Adjusting for truncation of the most recent data | Projecting the reproduction number with the Gaussian Process | Fixed reproduction number | Breakpoints | Weekly random walk | No delays | Non-parametric infection model

Quick start | Defining a distribution | Uncertain parameters | Discretising | Combining distributions | Plotting | Sampling | Uncertain nonparametric distributions

Setup | The pipeline workflow | Assigning age groups | Surveys | Bootstrapping | Demography | Symmetric contact matrices | Contact rates per capita | Splitting contact matrices | Filtering | Participant weights | Temporal aspects and demography | User-defined participant weights | Weight threshold | Numerical example | Get survey data | Weight by day of week | Weight by age | Apply threshold | Plotting | Using ggplot2 | Using R base | References

Usage | Using contact matrices with socialmixr | References

Background | Setup | Data | Estimating infections | Estimating secondary scaling and delay | Forecasting secondary outcomes

Introduction | Set up | Simulating censored delay data | Setting priors | Fitting the model | Checking parameter recovery

Data | Set up | Parameters | Delay distributions | Generation intervals | Reporting delays | Truncation | Completeness of reporting | Initial reproduction number | Weighing delay priors | Estimation and forecasting | Forecasting secondary outcomes | Interpretation | Evaluating forecasts with scoringutils

Quick start | Reporting delays, incubation period and generation time | epinow() | regional_epinow()

Running the model on a single region | Running the model simultaneously on multiple regions

Overview | Definition | Matérn 3/2 covariance kernel (the default) | Squared exponential kernel | Ornstein-Uhlenbeck (Matérn 1/2) kernel | Matérn 5/2 covariance kernel | Hilbert space approximation | Modelling the reproduction number | References

Packages | Data | Approach 1: Weekly timestep | Approach 2: Daily process, weekly reporting (fitted day-of-week) | Approach 3: Daily process, weekly reporting (structural) | Approach 4: Daily timestep | Comparison | Weekly scale | Daily scale | Runtime | Choosing an approach

Quick start | Package | Data | Filtering | Preprocessing | Visualising the data | Choosing a nowcast horizon | Nowcast target | The default model | Posterior predictions | Alternative models | Process model | Reference model: reporting delays | Fitting the alternative models | Results | Diagnostics | Comparing all models | Using package functions rather than S3 methods | Next steps

Overview | Setup | Model specifications | Fitting | NUTS with prior initialisation (default) | NUTS with pathfinder initialisation | Pathfinder (approximate inference) | Runtime comparison | Diagnostics | NUTS diagnostics | Pathfinder diagnostics | Nowcast comparison | Posterior parameter comparison | Updating with posterior-as-prior | Summary

Use case | What we have | What do we do | Getting setup | Introducing the data: COVID-19 hospitalisations in Germany | Overview | Data transformations | Filtering the data | Visualising the data | Model | Expected hospitalisations | Expected infections | Instantaneous reproduction number | Latent infections | Latent reporting delay and ascertainment | Specifying the model using epinowcast::enw_expectation() | Delay distribution | Defining the delay distribution | Specifying the model using epinowcast::enw_reference() | Observation model and nowcast | Defining the observation model | Specifying the model using epinowcast::enw_obs() | Fitting the model to COVID-19 hospitalisations in Germany | Preprocess the data | Fitting the epinowcast model | Specifying the fitting options | Compiling the model | Fitting the model | Visualising the Nowcast | Plotting the nowcast based on real-time data | Plotting the nowcast based on retrospective data | Posterior predictions for cases by date of positive test and report | Real-time and retrospective estimates of the effective reproduction number | Estimates of the delay from testing positive to hospitalisation both in real-time and retrospectively | Estimates of the number of expected hospitalisations both in real-time and retrospectively | Wrapping up | Summary | Strengths | Limitations | Alternative packages | References

Model | Priors

Introduction | Set up | Overview of all priors | estimate_infections() priors | estimate_secondary() priors | estimate_truncation() priors | Prior impacts and choice guidance | Reproduction number | Gaussian Process length scale | Gaussian Process magnitude | Random walk for $R_t$ (alternative to GP) | Observation model: overdispersion | Observation model: scaling | For estimate_infections(): | For estimate_secondary(): | Generation time distribution | Delays (incubation and reporting) | Truncation | Model choice in estimate_infections() | Priors for estimate_secondary() | Delay between primary and secondary | Priors for estimate_truncation() | Truncation distribution parameters | Practical workflow for prior specification | Step 1: Start with defaults | Step 2: Identify candidates for modification | Step 3: Modify one prior at a time | Step 4: Check prior predictive distributions | Step 5: Check model convergence | Common pitfalls and recommendations | Pitfall 1: Over-informative priors without justification | Pitfall 2: Ignoring generation time and delays | Pitfall 3: Estimating too many uncertain parameters | Pitfall 4: Wrong time scale for length scale | Pitfall 5: Forgetting the max parameter | References and further reading | Key papers

Model Overview | Disease natural history scenarios | Transmission scenarios with interventions | Presymptomatic transmission scenarios with interventions | Transmission in isolation | Model parameters | Further information

Introduction | Model overview | Specifying model components | Offspring distributions | Delay distributions | Event probabilities | Intervention options | Simulation controls | Running outbreak simulations | Visualising results | Summarising outcomes | Simplified COVID-19 contact tracing effectiveness analysis | Define epidemiological parameters | Run the simulation | {ringbp} Use Cases | References

Introduction | What an ARIMA term does | Using ARIMA terms in a formula | The kernel decomposition | Centring the integrated residual | Stationarity via partial autocorrelations | Group structure: dependent vs independent | Special cases | Priors | Where you can use it | Limitations | References

Setup | Random walk on weeks | Integrated AR | Stationary AR | Gaussian process on weeks | Independent per-(week, group) effects | Day-of-week effects | Combining latent and periodic terms | Moving-average components | Fit diagnostics | When to reach for which

Introduction | Decomposition into expected final notifications and report delay components | Expected final notifications | Default model | Generalised model | Instantaneous reproduction number/growth rate | Latent infections/notifications | Latent reporting delay and ascertainment | Delay distribution | Parametric baseline hazard | Non-parametric reference date effect $\delta_{g,t,d}$ and report date effect $\epsilon_{g,t,d}$ | Centring | Observation model and nowcast | Accounting for reported cases with a missing reference date | Implementation | Summary of module-parameter mappings | References

Use case | Other tools for delay estimation | Two ways to estimate a delay | Getting set up | Simulating a reporting triangle | Fitting the full model | Fitting the delay-only model | Comparing the recovered delay parameters | Comparing the recovered delay distribution | Recovering the delay from data with missing cells | Using the delay-only estimate to set priors | When to use the delay-only model | References

Overview | Core Capabilities | Different Timesteps and Timespans | Stratified and Multi-Group Nowcasting | Delay Modelling Approaches | Report Date Effects and Structural Reporting | Latent Process Models | Hierarchical Structure | Prior Specification | Missing Data Handling | Model Evaluation | Visualisation | Computational Options | Data Handling | Current Limitations | Further Reading

Available distributions | Discretisation and adjustment for maximum delay | Double interval censoring with primarycensored

Infection model | Renewal equation model | Initialisation | Infections | Time-varying reproduction number | Beyond the end of the observation period | Adjusting for susceptible population depletion | Non-Mechanistic infection model | Delays and scaling | Observation model | Truncation | References

Introduction | What a Gaussian process term does | Using Gaussian process terms in a formula | The kernel and Hilbert-space decomposition | Kernels and special cases | Group structure: dependent vs independent | Differencing order | Priors | Where you can use it | Limitations | References

Set up scenario parameter space | Parameter sweep across scenarios | Storing simulations with scenarios | Running scenarios in parallel

Overview | Data and notation | Likelihood | Continuous formulation | Truncation | Discrete observation likelihood | Untruncated approximation | Primary event distribution | Delay families and parameterisations | Priors | References

Component overview | Estimation models | Infection model | Secondary model | Truncation / nowcasting | Delay distribution fitting | Model configuration | Reproduction number | Gaussian process | Delay distributions | Observation model | Options summary | Forward simulation and forecasting | Simulation | Forecasting | Supporting utilities | Data preprocessing | Workflow wrappers | Stan backend

Introduction | Architecture | Relationship between models | Where to look next

Case studies | Public health surveillance | Literature | By package authors | By others

Setup | Data | Preprocessing | Latest observations | Cumulative reporting delay | Reporting delay heatmap | Reporting delay quantiles | Notifications by delay group | Using the individual plot functions | Helper functions

Epinowcast and Stan | Ensuring you have the proper toolchain | Now install CmdStanR and CmdStan | Epinowcast modelling | Installation | Running your first model | Setting enw_fit_opts | Investigating the quality of the model fit | Sampler settings | chains | threads_per_chain | iter_warmup and iter_sampling | max_treedepth | adapt_delta | Some decent defaults | Model settings | Setting priors | Exploring your data | Posterior predictions | Approaches to solve common problems | My model takes too long to run | Divergent transitions | My $\hat{R}$s are high and my esss are low | The posterior estimates are very wide | Other resources | Technical issues | Learning more about Stan and Bayesian inference

Introduction | Metrics for point forecasts | A note of caution | Absolute error | Squared error | Absolute percentage error | Binary forecasts | Brier score | Logarithmic score | Sample-based forecasts | CRPS | Overprediction, underprediction and dispersion | Log score | Dawid-Sebastiani score | Dispersion - Median Absolute Deviation (MAD) | Bias | Absolute error of the median | Squared error of the mean | Quantile-based forecasts | Weighted interval score (WIS) | Interval coverage | Interval coverage deviation | Quantile score | Additional metrics | Quantile coverage

Univariate forecasts | Multivariate forecasts | Multivariate point forecasts

Packages | Data | Data preprocessing | Models | Shared reporting delay distribution | Using the inflated posterior as a prior | Reference day of the week effect | Posterior predictions | Reporting day of the week effect | Age group variation | Variation based on reference date | Variation based on reference date stratified by age | Independent models for each age group. | Alternative models | Evaluation | Summary

Installation | Loading the package | Getting started | The bi_model class | Generating a dataset | The libbi class | Fitting a model to data using PMCMC | Analysing an MCMC run | Predictions | Sample observations | Filtering | Plotting | Saving and loading libbi objects | Creating libbi objects from previous runs | Debugging | Related packages | References

Functions plot_predictions() and make_na() | Function plot_interval_ranges() (formerly plot_ranges()) | Function plot_score_table()

Introduction | Usage | Load example data and split into train and test data | Get weights and create mixture | Score predictions | Methods | CRPS for one model and one single observation | CRPS for a mixture of all models and one single observation | Obtaining the weights that minimize CRPS | References

Definitions | Prerequisites | Example

merge_pred_and_obs()

Installation | Loading the package | Loading the model and generating a synthetic dataset | Adapt the number of particles | Adapt the proposal distribution | Compute DIC | Convert between LibBi times and actual times or dates | Create inference chains

Deterministic SIR model, observations of prevalence | Deterministic SIR model, observations of incidence | Stochastic SIR model (SDE), observations of incidence | Stochastic SIR model (jump), observations of incidence | Example observation data frame

Introduction | Forecast Rts, score and plot | Forecast cases, score and plot | Use iterative fitting to explore a forecast | Evaluate a model | Wrapper functions | Supporting generic modelling packages

Installing | Quantile lasso | Multiple quantiles | Tau x lambda grid | Other options