In this post, we will investigate the Metropolis-Hastings algorithm, which is still one of the most popular algorithms in the field of Markov chain Monte Carlo methods, even though its first appearence (see [1]) happened in 1953, more than 60 years in the past. It does for instance appear on the CiSe top ten list … Continue reading The Metropolis-Hastings algorithm

# Category: Markov chains

# Recurrent and ergodic Markov chains

Today, we will look in more detail into convergence of Markov chains - what does it actually mean and how can we tell, given the transition matrix of a Markov chain on a finite state space, whether it actually converges. So suppose that we are given a Markov chain on a finite state space, with … Continue reading Recurrent and ergodic Markov chains

# Finite Markov chains

In this post, we will look in more detail into an important class of Markov chains - Markov chains on finite state spaces. Many of the subtleties that are present when studying Markov chains in general state spaces do not appear in the finite case, while most of the key ideas and features of Markov … Continue reading Finite Markov chains

# Monte Carlo methods and Markov chains – an introduction

In our short series on machine learning, we have already applied sampling methods several times. We have used and implemented Gibbs sampling, and so far we have simply accepted that the approach works. Time to look at this in a bit more detail in order to understand why it works and what the limitations of … Continue reading Monte Carlo methods and Markov chains – an introduction