The Metropolis-Hastings algorithm

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

The difficulty in the bitcoin protocol

Mining is a challenge - a miner has to solve a mathematical puzzle to create a valid block and is rewarded with a certain bitcoin amount (12.5 at the time of writing) for investing electricity and computing power. But technology evolves, and the whole mining process would be pointless if the challenge could not be … Continue reading The difficulty in the bitcoin protocol

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