2014/06/20 by Sandra Fortini, Sonia Petrone, Fortini, Sandra +1
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #math.PR #stat.ME
paper · pdf · doi:10.48550/arxiv.1406.5421
To appear in Bernoulli Journal
arxiv created 2015/11/13 · arxiv updated 2015/11/16
Predictive constructions are a powerful way of characterizing the probability law 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 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 X. Under recurrence, Markov exchangeable processes are mixtures of Markov chains. Thus, our results help checking when a predictive scheme characterizes a prior for Bayesian inference on the unknown transition matrix of a Markov chain. 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.