Conditional exact tests for Markovianity and reversibility in multiple categorical sequences

We propose conditional exact tests based on sufficient statistics to compare exchangeability, Markov exchangeability, and Markov exchangeability of the reversible type, when data consist of several sequences of categorical data. As particular cases, we can compare three classes of mixture models (mixtures of i.i.d. sequences, mixtures of Markov chains and of reversible Markov chains) and we can test Markovianity and reversibility of a single sequence. © 2011 Sociedad de Estadística e Investigación Operativa