Flexible Extended State-Space Epidemiological Models with Modern Inference

An extended epidemiological modelling framework that goes beyond the classical SIR (Susceptible-Infectious-Recovered) model. Supports SEIR (Susceptible-Exposed-Infectious-Recovered), SEIRD (Susceptible-Exposed-Infectious-Recovered-Deceased), SVEIRD (Susceptible-Vaccinated-Exposed-Infectious-Recovered-Deceased), and age-stratified compartmental models with flexible intervention functions (spline-based, Gaussian process, or user-defined). Inference is available via maximum likelihood or sequential Monte Carlo (SMC, also known as particle filtering) with no external binary dependencies. Includes a dependency-free real-time effective reproduction number (Rt) estimator, spatial multi-patch models with gravity-model mobility, ensemble forecasting via Bayesian model averaging (BMA), and proper scoring rules including CRPS (Continuous Ranked Probability Score), coverage, and MAE (Mean Absolute Error) for forecast evaluation. Methods follow Anderson and May (1991, ISBN:9780198545996), Doucet, de Freitas, and Gordon (2001) , Cori et al. (2013) , and Gneiting and Raftery (2007) .

Bayesian Change-Point Detection and Time Series Decomposition

BEAST is a Bayesian estimator of abrupt change, seasonality, and trend for decomposing univariate time series and 1D sequential data. Interpretation of time series depends on model choice; different models can yield contrasting or contradicting estimates of patterns, trends, and mechanisms. BEAST alleviates this by abandoning the single-best-model paradigm and instead using Bayesian model averaging over many competing decompositions. It detects and characterizes abrupt changes (changepoints, breakpoints, structural breaks, joinpoints), cyclic or seasonal variation, and nonlinear trends. BEAST not only detects when changes occur but also quantifies how likely the changes are true. It estimates not just piecewise linear trends but also arbitrary nonlinear trends. BEAST is generically applicable to any real-valued time series, such as those from remote sensing, economics, climate science, ecology, hydrology, and other environmental and biological systems. Example applications include identifying regime shifts in ecological data, mapping forest disturbance and land degradation from satellite image time series, detecting market trends in economic indicators, pinpointing anomalies and extreme events in climate records, and analyzing system dynamics in biological time series. Details are given in Zhao et al. (2019) .

All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

Multivariate Time Series (MTS) is a general package for analyzing multivariate linear time series and estimating multivariate volatility models. It also handles factor models, constrained factor models, asymptotic principal component analysis commonly used in finance and econometrics, and principal volatility component analysis. (a) For the multivariate linear time series analysis, the package performs model specification, estimation, model checking, and prediction for many widely used models, including vector AR models, vector MA models, vector ARMA models, seasonal vector ARMA models, VAR models with exogenous variables, multivariate regression models with time series errors, augmented VAR models, and Error-correction VAR models for co-integrated time series. For model specification, the package performs structural specification to overcome the difficulties of identifiability of VARMA models. The methods used for structural specification include Kronecker indices and Scalar Component Models. (b) For multivariate volatility modeling, the MTS package handles several commonly used models, including multivariate exponentially weighted moving-average volatility, Cholesky decomposition volatility models, dynamic conditional correlation (DCC) models, copula-based volatility models, and low-dimensional BEKK models. The package also considers multiple tests for conditional heteroscedasticity, including rank-based statistics. (c) Finally, the MTS package also performs forecasting using diffusion index , transfer function analysis, Bayesian estimation of VAR models, and multivariate time series analysis with missing values.Users can also use the package to simulate VARMA models, to compute impulse response functions of a fitted VARMA model, and to calculate theoretical cross-covariance matrices of a given VARMA model.

Bayesian Optimal INterval (BOIN) Design for Single-Agent and Drug- Combination Phase I Clinical Trials

The Bayesian optimal interval (BOIN) design is a novel phase I clinical trial design for finding the maximum tolerated dose (MTD). It can be used to design both single-agent and drug-combination trials. The BOIN design is motivated by the top priority and concern of clinicians when testing a new drug, which is to effectively treat patients and minimize the chance of exposing them to subtherapeutic or overly toxic doses. The prominent advantage of the BOIN design is that it achieves simplicity and superior performance at the same time. The BOIN design is algorithm-based and can be implemented in a simple way similar to the traditional 3+3 design. The BOIN design yields an average performance that is comparable to that of the continual reassessment method (CRM, one of the best model-based designs) in terms of selecting the MTD, but has a substantially lower risk of assigning patients to subtherapeutic or overly toxic doses. For tutorial, please check Yan et al. (2020) .

Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

Perform fundamental analyses using Bayesian parametric and non-parametric inference (regression, anova, 1 and 2 sample inference, non-parametric tests, etc.). (Practically) no Markov chain Monte Carlo (MCMC) is used; all exact finite sample inference is completed via closed form solutions or else through posterior sampling automated to ensure precision in interval estimate bounds. Diagnostic plots for model assessment, and key inferential quantities (point and interval estimates, probability of direction, region of practical equivalence, and Bayes factors) and model visualizations are provided. Bayes factors are computed either by the Savage Dickey ratio given in Dickey (1971) or by Chib's method as given in xxx. Interpretations are from Kass and Raftery (1995) . ROPE bounds are based on discussions in Kruschke (2018) . Methods for determining the number of posterior samples required are described in Doss et al. (2014) . Bayesian model averaging is done in part by Feldkircher and Zeugner (2015) . Methods for contingency table analysis is described in Gunel et al. (1974) . Variational Bayes (VB) methods are described in Salimans and Knowles (2013) . Mediation analysis uses the framework described in Imai et al. (2010) . The loss-likelihood bootstrap used in the non-parametric regression modeling is described in Lyddon et al. (2019) . Non-parametric survival methods are described in Qing et al. (2023) . Methods used for the Bayesian Wilcoxon signed-rank analysis is given in Chechile (2018) and for the Bayesian Wilcoxon rank sum analysis in Chechile (2020) . Correlation analysis methods are carried out by Barch and Chechile (2023) , and described in Lindley and Phillips (1976) and Chechile and Barch (2021) . See also Chechile (2020, ISBN: 9780262044585).

Plotting for Bayesian Models

Plotting functions for posterior analysis, MCMC diagnostics, prior and posterior predictive checks, and other visualizations to support the applied Bayesian workflow advocated in Gabry, Simpson, Vehtari, Betancourt, and Gelman (2019) . The package is designed not only to provide convenient functionality for users, but also a common set of functions that can be easily used by developers working on a variety of R packages for Bayesian modeling, particularly (but not exclusively) packages interfacing with 'Stan'.

Bayesian Marginal Effects for 'brms' Models

Calculate Bayesian marginal effects, average marginal effects, and marginal coefficients (also called population averaged coefficients) for models fit using the 'brms' package including fixed effects, mixed effects, and location scale models. These are based on marginal predictions that integrate out random effects if necessary (see for example and ).

Adjust Longitudinal Regression Models Using Bayesian Methodology

Adjusts longitudinal regression models using Bayesian methodology for covariance structures of composite symmetry (SC), autoregressive ones of order 1 AR (1) and autoregressive moving average of order (1,1) ARMA (1,1).

High-Dimensional Model Selection

Model selection and averaging for regression, generalized linear models, generalized additive models, graphical models and mixtures, focusing on Bayesian model selection and information criteria (Bayesian information criterion etc.). See Rossell (2025) (see the URL field below for its URL) for a hands-on book describing the methods, examples and suggested citations if you use the package.

Combining Subset MCMC Samples to Estimate a Posterior Density

See Miroshnikov and Conlon (2014) . Recent Bayesian Markov chain Monto Carlo (MCMC) methods have been developed for big data sets that are too large to be analyzed using traditional statistical methods. These methods partition the data into non-overlapping subsets, and perform parallel independent Bayesian MCMC analyses on the data subsets, creating independent subposterior samples for each data subset. These independent subposterior samples are combined through four functions in this package, including averaging across subset samples, weighted averaging across subsets samples, and kernel smoothing across subset samples. The four functions assume the user has previously run the Bayesian analysis and has produced the independent subposterior samples outside of the package; the functions use as input the array of subposterior samples. The methods have been demonstrated to be useful for Bayesian MCMC models including Bayesian logistic regression, Bayesian Gaussian mixture models and Bayesian hierarchical Poisson-Gamma models. The methods are appropriate for Bayesian hierarchical models with hyperparameters, as long as data values in a single level of the hierarchy are not split into subsets.