Bayesian Analysis Of Linear Models Research Articles

Bayesian analysis of linear models exhibiting changes in mean and precisionat an unknown time point

This paper analyses a linear model in which both the mean and the precision change exactly once at an unknown point in time. Posterior distributions are found for the unknown time point at which the changes occurred and for the ratio of the precisions. The Bayesian predictive distribution of k future observations is also derived. It is shown that the unconditional posterior distribution of the ratio of precisions is a mixture of F-type distributions and the predictive distribution is a mixture of multivariate t distributions.

Bayesian Analysis of Linear Models.

Bayesian Analysis of Linear Models.

Bayesian Analysis of Linear Models.

Bayesian Analysis of Linear Models.

Bayesian Analysis of Linear Models.

Bayesian Analysis of Linear Models.

Bayesian Analysis of Linear Models with Two Random Components with Special Reference to the Balanced Incomplete Block Design

Bayesian Analysis of Linear Models with Two Random Components with Special Reference to the Balanced Incomplete Block Design

BAYESIAN ANALYSIS OF LINEAR MODELS: FIXED EFFECTS

ABSTRACTBayesian analysis is a method of making inferences concerning a given process which allows prior beliefs and data concerning the statistical structure of the process to be combined with the results of present trials of the process into a posterior credibility distribution on the parameters characterizing the process. Credibility interval statements from this distribution are often of interest. In this paper, a technique for stating some such intervals for a normal regression model is developed.Section 1 of this paper briefly presents an approach to Bayesian inference, due to Novick and Hall, which provides a technique for quantifying prior beliefs.Section 2 reviews the distribution theory necessary for Bayesian analysis of processes which are of the normal, linear fixed effects model type and presents a method of deriving Bayesian credibility intervals based on this distribution theory.Section 3 demonstrates the application of these methods to three sets of data.