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.

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 ...

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, < http://www3.stat.sinica.edu.tw/statistica/j6n4/j6n43/j6n43.htm>). Gronau, Singmann, & Wagenmakers (2020) .

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.

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).

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 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.

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, .

Bayes Nets: 'RHugin' Emulation with 'gRain'

Wrappers for functions in the 'gRain' package to emulate some 'RHugin' functionality, allowing the building of Bayesian networks consisting on discrete chance nodes incrementally, through adding nodes, edges and conditional probability tables, the setting of evidence, both 'hard' (boolean) or 'soft' (likelihoods), querying marginal probabilities and normalizing constants, and generating sets of high-probability configurations. Computations will typically not be so fast as they are with 'RHugin', but this package should assist users without access to 'Hugin' to use code written to use 'RHugin'.

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(). A detailed introduction to the package is provided by Willwerscheid and Stephens (2021) .