Countable Partially Exchangeable Mixtures

TL;DR

This paper characterizes countably mixed partially exchangeable sequences using hidden Markov models, providing a detailed description for both discrete and Polish valued sequences, thus advancing understanding of their structure.

Contribution

It introduces a characterization of countably mixed partially exchangeable sequences through a subclass of hidden Markov models, extending previous results to new settings.

Findings

Countably mixed sequences are characterized via hidden Markov models.

The results apply to both discrete and Polish valued sequences.

Provides a framework for understanding the structure of these sequences.

Abstract

Partially exchangeable sequences representable as mixtures of Markov chains are completely specified by de Finetti's mixing measure. The paper characterizes, in terms of a subclass of hidden Markov models, the partially exchangeable sequences with mixing measure concentrated on a countable set, both for discrete valued and for Polish valued sequences.