Bernoulli

  • Bernoulli
  • Volume 23, Number 3 (2017), 1538-1565.

Predictive characterization of mixtures of Markov chains

Sandra Fortini and Sonia Petrone

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Abstract

Predictive constructions are a powerful way of characterizing the probability laws of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are available, the predictive characterization implicitly defines the prior distribution, starting from assumptions on the observables; moreover, it often helps in designing efficient computational strategies. In this paper we give necessary and sufficient conditions on the sequence of predictive distributions such that they characterize a Markov exchangeable probability law for a discrete valued process $\mathbf{X}$. Under recurrence, Markov exchangeable processes are mixtures of Markov chains. Our predictive conditions are in some sense minimal sufficient conditions for Markov exchangeability; we also provide predictive conditions for recurrence. We illustrate their application in relevant examples from the literature and in novel constructions.

Article information

Source
Bernoulli, Volume 23, Number 3 (2017), 1538-1565.

Dates
Received: May 2014
Revised: April 2015
First available in Project Euclid: 17 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1489737617

Digital Object Identifier
doi:10.3150/15-BEJ787

Mathematical Reviews number (MathSciNet)
MR3624870

Zentralblatt MATH identifier
06714311

Keywords
Bayesian inference edge reinforced random walks Markov exchangeability predictive distributions recurrence reinforced processes

Citation

Fortini, Sandra; Petrone, Sonia. Predictive characterization of mixtures of Markov chains. Bernoulli 23 (2017), no. 3, 1538--1565. doi:10.3150/15-BEJ787. https://projecteuclid.org/euclid.bj/1489737617


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