Density Estimation via Bayesian Inference Engines

Bayesian density estimates for univariate continuous random samples are provided using the Bayesian inference engine paradigm. The engine options are: Hamiltonian Monte Carlo, the no U-turn sampler, semiparametric mean field variational Bayes and slice sampling. The methodology is described in Wand and Yu (2020) .

Bayesian Model Averaging for Random and Fixed Effects Meta-Analysis

Computes the posterior model probabilities for standard meta-analysis models (null model vs. alternative model assuming either fixed- or random-effects, respectively). These posterior probabilities are used to estimate the overall mean effect size as the weighted average of the mean effect size estimates of the random- and fixed-effect model as proposed by Gronau, Van Erp, Heck, Cesario, Jonas, & Wagenmakers (2017, ). The user can define a wide range of non-informative or informative priors for the mean effect size and the heterogeneity coefficient. Moreover, using pre-compiled Stan models, meta-analysis with continuous and discrete moderators with Jeffreys-Zellner-Siow (JZS) priors can be fitted and tested. This allows to compute Bayes factors and perform Bayesian model averaging across random- and fixed-effects meta-analysis with and without moderators. For a primer on Bayesian model-averaged meta-analysis, see Gronau, Heck, Berkhout, Haaf, & Wagenmakers (2021, ).

Bayesian Restricted Mean Survival Time for Cluster Effect

The parametric Bayes analysis for the restricted mean survival time (RMST) with cluster effect, as described in Hanada and Kojima (2024) . Bayes estimation with random-effect and frailty-effect can be applied to several parametric models useful in survival time analysis. The RMST under these parametric models can be computed from the obtained posterior samples.

Bayesian Change-Point Detection for Process Monitoring with Fault Detection

Bayes Watch fits an array of Gaussian Graphical Mixture Models to groupings of homogeneous data in time, called regimes, which are modeled as the observed states of a Markov process with unknown transition probabilities. In doing so, Bayes Watch defines a posterior distribution on a vector of regime assignments, which gives meaningful expressions on the probability of every possible change-point. Bayes Watch also allows for an effective and efficient fault detection system that assesses what features in the data where the most responsible for a given change-point. For further details, see: Alexander C. Murph et al. (2023) .

Bayesian Analysis of Replication Studies

Provides tools for the analysis of replication studies using Bayes factors (Pawel and Held, 2022) .

Bayesian reconstruction of growth velocity

A nonparametric empirical Bayes method for recovering gradients (or growth velocities) from observations of smooth functions (e.g., growth curves) at isolated time points.

Multivariate Adaptive Shrinkage

Implements the multivariate adaptive shrinkage (mash) method of Urbut et al (2019) for estimating and testing large numbers of effects in many conditions (or many outcomes). Mash takes an empirical Bayes approach to testing and effect estimation; it estimates patterns of similarity among conditions, then exploits these patterns to improve accuracy of the effect estimates. The core linear algebra is implemented in C++ for fast model fitting and posterior computation.

Large-Scale Bayesian Variable Selection Using Variational Methods

Fast algorithms for fitting Bayesian variable selection models and computing Bayes factors, in which the outcome (or response variable) is modeled using a linear regression or a logistic regression. The algorithms are based on the variational approximations described in "Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies" (P. Carbonetto & M. Stephens, 2012, ). This software has been applied to large data sets with over a million variables and thousands of samples.

EAP Scoring in Exploratory FA Solutions with Correlated Residuals

Obtaining Bayes Expected A Posteriori (EAP) individual score estimates based on linear and non-linear extended Exploratoy Factor Analysis solutions that include a correlated-residual structure.

Pathway Analysis Methods for Genomewide Association Data

Bayesian hierarchical methods for pathway analysis of genomewide association data: Normal/Bayes factors and Sparse Normal/Adaptive lasso. The Frequentist Fisher's product method is included as well.