A Mass-Shifting Phenomenon of Truncated Multivariate Normal Priors

tmvtnorm: A Package for the Truncated Multivariate Normal Distribution

Abstract In this article we present tmvtnorm, an R package implementation for the truncated multivariate normal distribution. We consider random number generation with rejection and Gibbs sampling, computation of marginal densities as well as computation of the mean and covariance of the truncated variables. This contribution brings together latest research in this field and provides useful met...

Objective Priors for the Bivariate Normal Model with Multivariate Generalizations

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., Bayesian, frequentist, fiducial), and the criteria involved in deciding on optimal objective priors (e.g., ease of computation, frequentist pe...

Optimal direction Gibbs sampler for truncated multivariate normal distributions

Generalized Gibbs samplers simulate from any direction, not necessarily limited to the coordinate directions of the parameters of the objective function. We study how to optimally choose such directions in a random scan Gibbs sampler setting. We consider that optimal directions will be those that minimize the Kullback-Leibler divergence of two Markov chain Monte Carlo steps. Two distributions o...

The Stein phenomenon for monotone incomplete multivariate normal data

We establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from Np+q(μ,Σ), a (p+ q)-dimensional multivariate normal population with mean μ and covariance matrix Σ. On the basis of data consisting of n observations on all p+q characteristics and an additional N − n observations on the last q characteristics, where all observations are mutually independent, denot...

Screening for a Multivariate Mixture Normal Distribution