4. The MCMC module

This module is the original part of the program, although massively rewritten from version 1.0.4 to 1.1. Originally, EPIC could run with standard MCMC sampler or Parallel-Tempering MCMC. The former has been temporarily removed to give place to a new and cleaner implementation attempting to solve some bugs. Use version 1.0.4 in case you need it. The MCMC sampler comes with an experimental adaptive routine that adjusts the covariance of the proposal multivariate Gaussian probability density for optimal efficiency, aiming at an acceptance rate around \(0.234\). In the following sections I briefly introduce the MCMC method and show how to use this program to perform simulations, illustrating with examples.

• 4.1. Introduction to MCMC and the Bayesian method
  • The Bayes Theorem
  • The Metropolis-Hastings sampler
  • The Parallel Tempering algorithm (removed in this version)
• 4.2. Before starting
  • Changing the default working directory
  • The structure of the .ini file
• 4.3. Running MCMC
  • Sampling the posterior distribution
  • Adaptation (beta)
  • Analyzing the chains
    • Additional options
  • Making the triangle plots
    • Additional options
    • Combining two or more simulations in one plot
    • Visualizing chain sequences and convergence