Statistical inference for truncated Dirichlet distribution and its application in misclassification

Abstract

This paper is concerned with the statistical inference of a truncated Dirichlet distribution (TDD) arising in the general context of misclassified multinomial models (such as medical screening or diagnostic tests) and experimental design with mixtures. By employing the conditional distribution method, we offer a generating procedure for the TDD. Alternatively, a sampling-based approach using the Gibbs sampler was provided as a means for developing the posterior moments of interest. Finding the mode of a TDD is equivalent to extracting the constrained maximum likelihood estimate (MLE) of parameter vector in a multinomial model. Based upon a theoretic result, we propose an algorithm to calculate the constrained MLE. Applications in misclassification are presented.