Open Access
August 2017 Predictive characterization of mixtures of Markov chains
Sandra Fortini, Sonia Petrone
Bernoulli 23(3): 1538-1565 (August 2017). DOI: 10.3150/15-BEJ787


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.


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Sandra Fortini. Sonia Petrone. "Predictive characterization of mixtures of Markov chains." Bernoulli 23 (3) 1538 - 1565, August 2017.


Received: 1 May 2014; Revised: 1 April 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714311
MathSciNet: MR3624870
Digital Object Identifier: 10.3150/15-BEJ787

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

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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