Visualizing a Markov Chain

A Markov Chain describes a sequence of states where the probability of transitioning from states depends only the current state. Markov chains are useful in a variety of computer science, mathematics, and probability contexts, also featuring prominently in Bayesian computation as Markov Chain Monte Carlo. Here, we’re going to look at a relatively simple breed of Markov chain and build up some intuition using simulations and animations (two of my favorite things).

An Intuitive Look at Binomial Probability in a Bayesian Context

Binomial probability is the relatively simple case of estimating the proportion of successes in a series of yes/no trials. The perennial example is estimating the proportion of heads in a series of coin flips where each trial is independent and has possibility of heads or tails. Because of its relative simplicity, the binomial case is a great place to start when learning about Bayesian analysis. In this post, I will provide a gentle introduction to Bayesian analysis using binomial probability as an example.