Monte Carlo Markov Chains

Abstract

Monte Carlo Markov Chains (MCMC) are a powerful method to analyze scientific data that has become popular with the availability of modern-day computing resources. The basic idea behind an MCMC is to determine the probability distribution function of quantities of interest, such as model parameters, by repeatedly querying datasets used for their measurement. The resulting sequence of values form a Markov chain that can be analyzed to find best-fit values and confidence intervals. The modern-day data analyst will find that MCMCs are an essential tool that permits tasks that are simply not possible with other methods, such as the simultaneous estimate of parameters for multi-parametric models of virtually any level of complexity, even in the presence of correlation among the parameters.