Let X|μ ∼ Np(μ,vxI ) and Y |μ ∼ Np(μ,vyI ) be independent pdimensional multivariate normal vectors with common unknown mean μ. Based on observing X = x, we consider the problem of estimating the true predictive density p(y|μ) of Y under expected Kullback–Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Baye...

To appear in Theory and Practice of Logic Programming (TPLP) This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give several nontrivial examples and illustrate the use of P-log for knowledge representation and up...

This paper is the second in a series of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In the first paper1, the Bayes estimator for a function of a probability distribution was introduced, the optimal properties of the Bayes estimator were discussed, and the Bayes and frequency-counts estimators for the Shannon entrop...

In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfolio. When the prior knowledge is vague, the E-Bayesian and robust Bayesian analysis can be used to handle the uncertainty in specifying the prior distribution by considering a class of priors instead of a single prior. In th...

This dissertation aims at applying the novel formalism of Random Set Theory (RST) to some problems in communication theory: tracking of mobile users that are continuously entering and leaving a wireless network and tracking of abruptly time-varying channel where multipath components are free to appear and disappear. RST allows to solve both problems in an unified framework through Bayes recursi...

In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten and Tibshirani, 2011, Cai and Liu, 2011, Mai et al., 2012 and Fan et al., 2012). In this paper, we develop high-dimensional sparse semiparametric discriminant analysis (SSDA) that generalizes the normal-theory discr...

In this paper, the well-known proportional hazards model which includes several well-known lifetime distributions such as exponential,Pareto, Lomax, Burr type XII, and so on is considered. With both Bayesian and non-Bayesian approaches , we consider the estimation of parameters of interest based on progressively Type-II right censored samples. The Bayes estimates are obtained based on symmetric...

This paper is the second in a series of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In the first paper1, the Bayes estimator for a function of a probability distribution was introduced, the optimal properties of the Bayes estimator were discussed, and the Bayes and frequency-counts estimators for the Shannon entrop...