We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the unknown mean is fixed, the covariance of future samples can be different from training samples. We show that the Bayesian predictive distribution based on the u...

In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the `1 norm of horizontal and vertical first order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (SAR) prior. Since, for a given obs...

It is becoming more typical in regression problems today to have the situation where “p > n”, that is, where the number of covariates is greater than the number of observations. Approaches to this problem include such strategies as model selection and dimension reduction, and, of course, a Bayesian approach. However, the discrepancy between p and n can be so large, especially in genomic data, t...

Two measures of the influence of the prior distribution p(θ) in Bayes estimation are proposed. Both involve comparing with alternative priors proportional to p(θ), for s ≥ 0. The first one, the influence curve for the prior distribution is simply the curve of parameter values which are obtained as estimates when the estimation is made using p(θ) instead of p(θ). It measures the overall influenc...

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori, the likelihood function captur...

In situations where noisy signals of some underlying variable are observed, Paul Milgrom (The Bell Journal of Economics, 12(2): 380–391) showed that a higher signal implies a higher posterior (in the sense of first-order stochastic dominance) for every non-degenerate prior if and only if the conditional distribution satisfies the strict monotone likelihood ratio property (MLRP). We show that fo...

A previous investigation by Lambert et al., which used computer simulation to examine the influence of choice of prior distribution on inferences from Bayesian random effects meta-analysis, is critically examined from a number of viewpoints. The practical example used is shown to be problematic. The various prior distributions are shown to be unreasonable in terms of what they imply about the j...

We previously introduced a new Bayesian predictive classification (BPC) approach to robust speech recognition and showed that BPC is capable of coping with many types of distortions. We also learned that the efficacy of the BPC algorithm is inflEenced by the appropriateness of the prior distribution for the mismatch being compensated. If the prior distribution fails to characterize the variabil...