Generalized information criteria for optimal Bayes decisions
نویسندگان
چکیده
This paper deals with Bayesian models given by statistical experiments and standard loss functions. Bayes probability of error and Bayes risk are estimated by means of classical and generalized information criteria applicable to the experiment. The accuracy of the estimation is studied. Among the information criteria studied in the paper is the class of posterior power entropies which includes the Shannon entropy as a special case for the power α = 1. It is shown that the most accurate estimate is in this class achieved by the quadratic posterior entropy of the power α = 2. The paper introduces and studies also a new class of alternative power entropies which in general estimate the Bayes errors and risk more tightly than the classical power entropies. Concrete examples, tables and figures illustrate the obtained results.
منابع مشابه
Quasi-convexity and optimal binary fusion for distributed detection with identical sensors in generalized Gaussian noise
In this correspondence, we present a technique to find the optimal threshold for the binary hypothesis detection problem with identical and independent sensors. The sensors all use an identical and single threshold to make local decisions, and the fusion center makes a global decision based on the local binary decisions. For generalized Gaussian noises and some non-Gaussian noise distributions,...
متن کاملGeneralized information criteria for optimal Bayes decisons
This report constitutes an unrefereed manuscript which is intended to be submitted for publication. Any opinions and conclusions expressed in this report are those of the author(s) and do not necessarily represent the views of the Institute. This paper deals with Bayesian models given by statistical experiments and common types of loss functions. Probability of error of the Bayes identificator ...
متن کاملAdaptive Bayesian Criteria in Variable Selection for Generalized Linear Models
For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be computed easily and quickly. The performance of these criteria is assessed via simulation and compared to othe...
متن کاملA Hierarchical Bayes Approach to Variable Selection for Generalized Linear Models
For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be computed easily and quickly. The performance of these criteria is assessed via simulation and compared to othe...
متن کاملContextual Bandits: Approximated Linear Bayes for Large Contexts
Contextual bandits, and in general informed decision making, can be studied in the general stochastic/statistical setting by means of the conditional probability paradigm where Bayes’ theorem plays a central role. However, when informed decisions have to be made considering very large contextual information or the information is contained in too many variables with large history of observations...
متن کامل