A generalization of multivariate total positivity of order two with an application to a Bayesian learning procedure

Abstract

This paper investigates to generalize the MTP2 (multivariate total positivity of order two), and deals with the Bayesian learning procedure for sequential decision problems on a partially observable Markov process as an application of this property. This property has an order preserving property for the expectation of a non-decreasing function. As for a partially observable Markov process, all informations are summarized by probability measures on the state space. Among informations, an order is induced by means of the generalized MTP2. We employ the Bayes’ theorem as the learning procedure, and investigate the sequential decision problems under two assumptions. There also exist some relationships between prior and posterior information. These properties are essential for observing the sequential decision problems on this process.