Método de Monte Carlo : uso y aplicaciones en Inferencia Bayesiana

Abstract

It’s sure that, nowadays, Statistics is one of the most applicable areas in Math ematics. Because of that, it’s so important to study new methods to allow as to improve this important discipline. So this research work borns from the neccesity of predicting future events, under the knowledge of past events. First, it will be introduced some definitions and results about Bayesian Statistics and Markov chains. This will be shown in a discrete way, althought we will use them in continuous form. Talking about the algorithm, it will be presented how it works, and what prop erties it follows, seeing that it generates a Markov chain, and some variants. We’ll see that this algorithm is the one to be used to simulate samples from unknown distributions. Later, it’ll be introduced the Gibbs sampler, that will be used to simulate sample from that functions that, ones you fixed their values, we’ll obtain easy simple forms. Then, we will learn something about other methods like slice sampling or Hamiltonian dynamics. At last, we’ll be into a real-life example. It’s about studying the number of electric failure happened in a set of trains from 1992 to 1998, in order to calculate predictions about what number of failures will take place in a future. It well be seen, Bayesian Statistics will be used to estimate futures failures.