Computation of Bayes Factors for Common Designs

A suite of functions for computing various Bayes factors for simple designs, including contingency tables, one- and two-sample designs, one-way designs, general ANOVA designs, and linear regression.

Bridge Sampling for Marginal Likelihoods and Bayes Factors

Provides functions for estimating marginal likelihoods, Bayes factors, posterior model probabilities, and normalizing constants in general, via different versions of bridge sampling (Meng & Wong, 1996, < https://www3.stat.sinica.edu.tw/statistica/j6n4/j6n43/j6n43.htm>). Gronau, Singmann, & Wagenmakers (2020) .

Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien

Functions for latent class analysis, short time Fourier transform, fuzzy clustering, support vector machines, shortest path computation, bagged clustering, naive Bayes classifier, generalized k-nearest neighbour ...

Methods for Adaptive Shrinkage, using Empirical Bayes

The R package 'ashr' implements an Empirical Bayes approach for large-scale hypothesis testing and false discovery rate (FDR) estimation based on the methods proposed in M. Stephens, 2016, "False discovery rates: a new deal", . These methods can be applied whenever two sets of summary statistics---estimated effects and standard errors---are available, just as 'qvalue' can be applied to previously computed p-values. Two main interfaces are provided: ash(), which is more user-friendly; and ash.workhorse(), which has more options and is geared toward advanced users. The ash() and ash.workhorse() also provides a flexible modeling interface that can accommodate a variety of likelihoods (e.g., normal, Poisson) and mixture priors (e.g., uniform, normal).

High Performance Implementation of the Naive Bayes Algorithm

In this implementation of the Naive Bayes classifier following class conditional distributions are available: 'Bernoulli', 'Categorical', 'Gaussian', 'Poisson', 'Multinomial' and non-parametric representation of the class conditional density estimated via Kernel Density Estimation. Implemented classifiers handle missing data and can take advantage of sparse data.

Empirical Bayes Thresholding and Related Methods

Empirical Bayes thresholding using the methods developed by I. M. Johnstone and B. W. Silverman. The basic problem is to estimate a mean vector given a vector of observations of the mean vector plus white noise, taking advantage of possible sparsity in the mean vector. Within a Bayesian formulation, the elements of the mean vector are modelled as having, independently, a distribution that is a mixture of an atom of probability at zero and a suitable heavy-tailed distribution. The mixing parameter can be estimated by a marginal maximum likelihood approach. This leads to an adaptive thresholding approach on the original data. Extensions of the basic method, in particular to wavelet thresholding, are also implemented within the package.

Bayes Factors for Informative Hypotheses

Computes approximated adjusted fractional Bayes factors for equality, inequality, and about equality constrained hypotheses. For a tutorial on this method, see Hoijtink, Mulder, van Lissa, & Gu, (2019) . For applications in structural equation modeling, see: Van Lissa, Gu, Mulder, Rosseel, Van Zundert, & Hoijtink, (2021) . For the statistical underpinnings, see Gu, Mulder, and Hoijtink (2018) ; Hoijtink, Gu, & Mulder, J. (2019) ; Hoijtink, Gu, Mulder, & Rosseel, (2019) .

Empirical Bayes Estimation and Inference

Kiefer-Wolfowitz maximum likelihood estimation for mixture models and some other density estimation and regression methods based on convex optimization. See Koenker and Gu (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1--26, .

Solve the Empirical Bayes Normal Means Problem

Provides simple, fast, and stable functions to fit the normal means model using empirical Bayes. For available models and details, see function ebnm(). Our JSS article, Willwerscheid, Carbonetto, and Stephens (2025) , provides a detailed introduction to the package.

Empirical Bayes Estimation Strategies

Empirical Bayes methods for learning prior distributions from data. An unknown prior distribution (g) has yielded (unobservable) parameters, each of which produces a data point from a parametric exponential family (f). The goal is to estimate the unknown prior ("g-modeling") by deconvolution and Empirical Bayes methods. Details and examples are in the paper by Narasimhan and Efron (2020, ).