On multivariate ridge regression

A multivariate linear regression model with q responses as a linear function ofpindependent variables ry,= + k is considered withapxqparameter matrix B. The least squares (or Maximum Likelihood for multivariate normal E) % % estimator of B is deficient in that it takes no account of the % "across regression" correlations, on the one hand, and ignores the famous Stein effect, on the other hand. A remedy was offered by Brown and Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting the model in a linear hierarchical framework, obtaining the Brown and Zidek multivariate ridge estimators., Efron and Morris' estimators of several normal mean vectors and Fearn's Bayesian estimators of growth curves as special cases. The unknown covariance cases result in an identifiability problem which is treated in a Bayesian fashion using conjugate priors. The method is then applied to forecasting the final election results from partial returns obtained at election night

Bayesian Analysis of Binary Data Subject to Misclassification

This paper considers estimation of success probabilities of categorical binary data subject to misclassification errors from the Bayesian point of view. It has been shown by Bross (1954) that sample proportions are in general biased estimates. This bias is a function of the amount of misclassification and can be substantial. Tenenbein (1970) proposed to eliminate the bias by subjecting a portion of the sample to both true and fallible classifiers, resulting in a 2 x 2 table, from which the misclassification rates can be estimated. The rationale is that fallible classifiers are inexpensive relative to infallible ones. Hence if only a part of the sample is measured by the infallible classifier one can obtain a more efficient estimate, for a given sampling budget, than by measuring the whole sample using the infallible classifier. In many contexts an infallible classifier is unavailable or prohibitively expensive. Bayesian methods then provide a useful approach for dealing with the conseq..