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.

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 ...

Bayes Screening and Model Discrimination

Bayes screening and model discrimination follow-up designs.

Boltzmann Bayes Learner

Supervised learning using Boltzmann Bayes model inference, which extends naive Bayes model to include interactions. Enables classification of data into multiple response groups based on a large number of discrete predictors that can take factor values of heterogeneous levels. Either pseudo-likelihood or mean field inference can be used with L2 regularization, cross-validation, and prediction on new data. .

Bayes Factor Functions

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. However, one drawback of Bayes factors is their dependence on prior specifications that define null and alternative hypotheses. Additionally, there are challenges in their computation. To address these issues, we define Bayes factor functions (BFFs) directly from common test statistics. BFFs express Bayes factors as a function of the prior densities used to define the alternative hypotheses. These prior densities are centered on standardized effects, which serve as indices for the BFF. Therefore, BFFs offer a summary of evidence in favor of alternative hypotheses that correspond to a range of scientifically interesting effect sizes. Such summaries remove the need for arbitrary thresholds to determine "statistical significance." BFFs are available in closed form and can be easily computed from z, t, chi-squared, and F statistics. They depend on hyperparameters "r" and "tau^2", which determine the shape and scale of the prior distributions defining the alternative hypotheses. For replicated designs, the "r" parameter in each function can be adjusted to be greater than 1. Plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies.

Empirical Bayes Ranking

Empirical Bayes ranking applicable to parallel-estimation settings where the estimated parameters are asymptotically unbiased and normal, with known standard errors. A mixture normal prior for each parameter is estimated using Empirical Bayes methods, subsequentially ranks for each parameter are simulated from the resulting joint posterior over all parameters (The marginal posterior densities for each parameter are assumed independent). Finally, experiments are ordered by expected posterior rank, although computations minimizing other plausible rank-loss functions are also given.

The Bayes Factor Playground

A lightweight modelling syntax for defining likelihoods and priors and for computing Bayes factors for simple one parameter models. It includes functionality for computing and plotting priors, likelihoods, and model predictions. Additional functionality is included for computing and plotting posteriors.

Naive Bayes Classifier

Predicts any variable in any categorical dataset for given values of predictor variables. If a dataset contains 4 variables, then any variable can be predicted based on the values of the other three variables given by the user. The user can upload their own datasets and select what variable they want to predict. A 'handsontable' is provided to enter the predictor values and also accuracy of the prediction is also shown.

Analysis of Geostatistical Data using Bayes and Empirical Bayes Methods

Functions to fit geostatistical data. The data can be continuous, binary or count data and the models implemented are flexible. Conjugate priors are assumed on some parameters while inference on the other parameters can be done through a full Bayesian analysis of by empirical Bayes methods.

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, ).