Monte Carlo Methods for Inference in High-Dimensional Systems
Modern Monte Carlo methods have their roots in the 1940s when Fermi, Ulam, von Neumann, Metropolis and others began to use random numbers to examine various problems in physics from a stochastic perspective [118, 413]. Since then, these methods have established themselves as powerful and indispensable tools in most branches of science. In general, the MC-method represents a particular type of numerical scheme based on random numbers to calculate properties of probabilistic models, which cannot be addressed by analytical means. Its wide-spread use derives from its versatility and ease of implementation and its scope of application has extended considerably due to the dramatic increase within the last 2–3 decades in accessible computer power. In this chapter we shall mainly focus on the Markov Chain Monte Carlo method (MCMC) as a tool for inference in high-dimensional probability models, with special attention to the simulation of bio-macromolecules.