On the extendibility of partially and Markov exchangeable binary sequences

TL;DR

This paper investigates the extendibility of finite partially and Markov exchangeable binary sequences, providing necessary and sufficient conditions for their extension, and clarifies the relationship between these two types of exchangeability.

Contribution

It offers a detailed analysis of finite exchangeable sequences, establishing conditions for extendibility and clarifying the differences between partial and Markov exchangeability.

Findings

Necessary and sufficient conditions for extendibility of finite sequences.

Finite Markov exchangeable sequences are not equivalent to partially exchangeable sequences.

Clarification of the relationship between partial and Markov exchangeability.

Abstract

In [Fortini et al., Stoch. Proc. Appl. 100 (2002), 147--165] it is demonstrated that a recurrent Markov exchangeable process in the sense of Diaconis and Freedman is essentially a partially exchangeable process in the sense of de Finetti. In case of finite sequences there is not such an equivalence. We analyze both finite partially exchangeable and finite Markov exchangeable binary sequences and formulate necessary and sufficient conditions for extendibility in both cases.