IPython Interactive Computing and Visualization Cookbook

Fitting a Bayesian model by sampling from a posterior distribution with a Markov chain Monte Carlo method

In this recipe, we illustrate a very common and useful method for characterizing a posterior distribution in a Bayesian model. Imagine that you have some data and you want to obtain information about the underlying random phenomenon. In a frequentist approach, you could try to fit a probability distribution within a given family of distributions, using a parametric method such as the maximum likelihood method. The optimization procedure would yield parameters that maximize the probability of observing the data if given the null hypothesis.

In a Bayesian approach, you consider the parameters themselves as random variables. Their prior distributions ...