Bayesian inference for stationary data on finite state spaces

TL;DR

This paper develops a Bayesian inference framework for stationary data on finite state spaces, using an inverse limit construction and an augmented sampling scheme to update the posterior based on empirical distances.

Contribution

It introduces a novel parametrization of stationary measures and an explicit prior model incorporating an additional sampling step for improved inference.

Findings

Provides a new parametrization of shift-ergodic measures

Defines an explicit prior model with augmented sampling

Demonstrates posterior update using empirical distance measurements

Abstract

In this work the issue of Bayesian inference for stationary data is addressed. Therefor a parametrization of a statistically suitable subspace of the the shift-ergodic probability measures on a Cartesian product of some finite state space is given using an inverse limit construction. Moreover, an explicit model for the prior is given by taking into account an additional step in the usual stepwise sampling scheme of data. An update to the posterior is defined by exploiting this augmented sample scheme. Thereby, its model-step is updated using a measurement of the empirical distances between the model classes.