The paper deals with the identification of a stationary autoregressive model for a time series and the contemporary detection of a change in its mean. We adopt the Bayesian approch with weak prior information about the parameters of the models under comparison and an exact form of the likelihood function. When necessary, we resort to fractional Bayes factor to choose between models, and to impo...

The Theory of Intrinsic Priors, developed by Berger and Pericchi (1996a,b), is a general method of constructing objective priors for testing and model selection when proper priors are considered for the simpler null hypotheses. When this prior distribution is improper, as is typically the case for Objective Bayesian testing, they suggest approximating the (improper) prior by a sequence of prope...

Generalized linear mixed models (GLMM) are used in situations where a number of characteristics (covariates) affect a nonnormal response variable and the responses are correlated. For example, in a number of biological applications, the responses are correlated due to common genetic or environmental factors. In many applications, the magnitude of the variance components corresponding to one or ...

The key quantity needed for Bayesian hypothesis testing and model selection is the marginal likelihood for a model, also known as the integrated likelihood, or the marginal probability of the data. In this paper we describe a way to use posterior simulation output to estimate marginal likelihoods. We describe the basic Laplace-Metropolis estimator for models without random eeects. For models wi...

The Bayesian interpretation of probability is one of two broad categories of interpretations. Bayesian inference updates knowledge about unknowns, parameters, with information from data. The LaplacesDemon package in R enables Bayesian inference, and this vignette provides an introduction to the topic. This article introduces Bayes’ theorem, model-based Bayesian inference, components of Bayesian...

Arange of approximatemethods have been proposed formodel choice based onBayesian principles, given the problems involved in multiple integration in multi-parameter problems. Formal Bayesian model assessment is based on prior model probabilities P(M = j) and posterior model probabilities P(M = j |Y ) after observing the data. An approach is outlined here that produces posterior model probabiliti...

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the ...

A major inference task in Bayesian networks is explaining why some variables are observed in their particular states using a set of target variables. Existing methods for solving this problem often generate explanations that are either too simple (underspecified) or too complex (overspecified). In this paper, we introduce a method called Most Relevant Explanation (MRE) which finds a partial ins...