Inferência em Cadeias de Markov: uma comparação numérica entre os métodos de estimação clássico e bayesiano

Abstract

A Markov chain is a type of stochastic process that can be used to model a sequence of random variables that we judge to be dependent on the most recent past. This work introduces the concept of inference in Markov chains in a finite state space, obtaining estimators of the transition probabilities in the frequentist context, furthermore, it introduces the concept of Bayesian inference and how we obtain the estimators with such an approach and finally, it compares the classical and Bayesian inferential methods in a stochastic process, trying to define which one has a better performance when estimating the transition probabilities of a Markov chain with two states in several scenarios.