Software for Bayesian Statistics

In this summary we introduce the papers published in the special issue on Bayesian statistics. This special issue comprises 20 papers on Bayesian statistics and Bayesian inference on different topics such as general packages for hierarchical linear model fitting, survival models, clinical trials, missing values, time series, hypothesis testing, priors, approximate Bayesian computation, and others.


Introduction
Bayesian computation has experienced a surge in recent years (see, for example, Martin, Frazier, and Robert 2020, for a thorough historical review of Bayesian computation), driven by both methodological and software developments. In particular, the development of new computational methods such as the integrated nested Laplace approximation (INLA), Hamiltonian Monte Carlo, sequential Monte Carlo, or variational Bayes (to mention a few) has paved the way to new software tools.
For these reasons, in December 2018 a call for papers for contributions on a special issue on Bayesian statistics was announced worldwide. In the end, 20 papers have been accepted to be included in this special issue. Contributed papers span a wide range of topics, including software for hierarchical linear model fitting, time series, survival models, epidemiology, hypothesis testing, priors, approximate Bayesian computation, and many others.
All but one paper use the R software (R Core Team 2021) and the R packages described in this special issue contribute to the already rich task view dedicated to "Bayesian Inference" (Park 2021) available from the Comprehensive R Archive Network at https://CRAN.R-project. org/view=Bayesian.

Model fitting
The special issue includes a number of packages for fitting Bayesian hierarchical models using different types of software. Van Niekerk, Bakka, Rue, and Schenk (2021) present new developments for the INLA package (Lindgren and Rue 2015) about complex joint survival models, non-separable space-time models and high performance computing to fit very large models faster. Similarly, Michaud, De Valpine, Turek, Paciorek, and Nguyen (2021) describe the implementation of algorithms for state-space model analysis using sequential Monte Carlo methods for the nimble software which have been included in the nimbleSMC package. The bamlss package is described in Umlauf, Klein, Simon, and Zeileis (2021) to fit Bayesian generalized additive models for location, scale and shape (GAMLSS models). Bürkner (2021) describes how to fit Bayesian item response models using Stan (Carpenter et al. 2017) and the R package brms (Bürkner 2017). Similarly, Merkle, Fitzsimmons, Uanhoro, and Goodrich (2021)

Hierarchical linear models
Certain papers describe fitting particular types of Bayesian models. Fasiolo, Wood, Zaffran, Nedellec, and Goude (2021) focus on fitting Bayesian nonparametric quantile regression models using R package qgam, which is an extension of the well-known mgcv package for fitting generalized additive models (Wood 2017). Bonner, Kim, Westneat, Mutzel, Wright, and Schofield (2021) show how to fit double hierarchical linear models with the dalmatian package, which relies on JAGS and nimble (de Valpine, Turek, Paciorek, Anderson-Bergman, Temple Lang, and Bodik 2017) for model fitting. The BayesSUR R package for high-dimensional multivariate Bayesian variable and covariance selection for seemingly unrelated regression models is described in Zhao, Banterle, Bottolo, Richardson, Lewin, and Zucknick (2021).

Time series
A couple of papers in this special issue focus on time series analysis. Hosszejni and Kastner (2021) present an update of R package stochvol (Kastner 2016) to fit univariate stochastic volatility (SV) models (that now can handle linear mean models, conditionally heavy tails, and the leverage effect in combination with SV) and describe the factorstochvol R package for multivariate SV models. Time-varying parameter (TVP) models using global-local shrinkage priors to avoid overfitting with the shrinkTVP R package are described in Knaus, Bitto-Nemling, Cadonna, and Frühwirth-Schnatter (2021). Kuschnig and Vashold (2021) fit vector auto-regression (VAR) models for multivariate time series with hierarchical prior selection using the R package BVAR. Mayrink, Duarte, and Demarqui (2021) describe the implementation of a new JAGS module that implements the piece-wise exponential distribution so that it can be used when defining models using the BUGS language (Lunn, Spiegelhalter, Thomas, and Best 2009). This distribution if often employed to model the baseline hazard function when fitting Cox proportional hazards models in survival analysis. Corradin, Canale, and Nipoti (2021) present the BNPmix R package for efficient Bayesian inference on nonparametric mixture models used for density estimation and clustering. Methods for model-based clustering of binary dissimilarity matrices implemented in the dmbc package are described in Venturini and Piccarreta (2021).

Hypothesis testing
Two papers in this special issue tackle the problem of hypothesis testing. Gronau, Raj K. N., and Wagenmakers (2021) show how to perform Bayesian inference for A/B tests using R package abtest, which allows for the incorporation of expert knowledge in the priors. Mulder et al. (2021) describe a general framework for testing hypotheses using Bayes factors for many different types of models. Weber, Li, Seaman, Kakizume, and Schmidli (2021) discuss the use of the meta-analytic predictive (MAP) approach to derive informative priors from historical data for clinical trials that has been implemented in the RBesT R package. Similarly, Eggleston, Ibrahim, McNeil, and Catellier (2021) describe the BayesCTDesign for the R programming language for twoarm randomized Bayesian clinical trials design, that can take advantage of historical control data when available. Erler, Rizopoulos, and Lesaffre (2021) deal with the problem of missing data and describe the JointAI R package to perform simultaneous analysis and imputation in regression models with incomplete covariates.
The applications presented in the papers to illustrate the software encompass a wide range of disciplines including biology, ecology, medicine, economics, and sociology. This shows that Bayesian methods are extremely versatile and can be applied to any real data problem when it is necessary to make inference on unknown quantities by taking properly into account all the uncertainty sources. We hope that the papers included in the special issue will inspire researchers new to the Bayesian approach but also more expert users who are looking for new (and hopefully more efficient) software.