Unified Bayesian and Conditional Frequentist Testing for Discrete Distributions
نویسنده
چکیده
Testing of hypotheses for discrete distributions is considered in this paper. The goal is to develop conditional frequentist tests that allow the reporting of datadependent error probabilities such that the error probabilities have a strict frequentist interpretation and also reflect the actual amount of evidence in the observed data. The resulting randomized tests are also seen to be Bayesian tests, in the strong sense that the reported error probabilities are also the posterior probabilities of the hypotheses. The new procedure is illustrated for a variety of testing situations, both simple and composite, involving discrete distributions. Testing linkage heterogeneity with the new procedure is given as an illustrative example.
منابع مشابه
Unified Conditional Frequentist and Bayesian Testing of Composite Hypotheses
Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data. The resulting tests are...
متن کاملConditional Frequentist Sequential Tests for the Drift of Brownian Motion
In this paper, we consider the problem of sequentially testing simple hypotheses concerning the drift of a Brownian motion process from a unified Bayesian and frequentist perspective. The conditional frequentist approach to testing statistical hypotheses has been utilized in a variety of settings to produce tests that are virtually equivalent to their objective Bayesian counterparts. Herein, we...
متن کاملComparison between Frequentist Test and Bayesian Test to Variance Normal in the Presence of Nuisance Parameter: One-sided and Two-sided Hypothesis
This article is concerned with the comparison P-value and Bayesian measure for the variance of Normal distribution with mean as nuisance paramete. Firstly, the P-value of null hypothesis is compared with the posterior probability when we used a fixed prior distribution and the sample size increases. In second stage the P-value is compared with the lower bound of posterior probability when the ...
متن کاملMCMC methods to approximate conditional predictive distributions
Sampling from conditional distributions is a problem often encountered in statistics when inferences are based on conditional distributions which are not of closed-form. Several Markov chain Monte Carlo (MCMC) algorithms to simulate from them are proposed. Potential problems are pointed out and some suitable modifications are suggested.Approximations based on conditioning sets are also explored...
متن کاملBayesian and Iterative Maximum Likelihood Estimation of the Coefficients in Logistic Regression Analysis with Linked Data
This paper considers logistic regression analysis with linked data. It is shown that, in logistic regression analysis with linked data, a finite mixture of Bernoulli distributions can be used for modeling the response variables. We proposed an iterative maximum likelihood estimator for the regression coefficients that takes the matching probabilities into account. Next, the Bayesian counterpart...
متن کامل