| Summary: | Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, pi, where either pi does not exist in closed form, or, if it does, there exist no efficient methods to simulate an independent sample from it. MCMC methods create an ergodic Markov chain {Xn, n = 1, 2...} with stationary distribution pi such that as n tends to infinity, the distribution of Xn approaches pi. A wealth of diagnostic tools for convergence assessment of MCMC methods have been proposed, yet none has proved to be completely dependable and easy to implement. This thesis will review the literature on MCMC algorithms and diagnostic tools, and it will present a new convergence assessment method based on the principle of detailed balance. Moreover, the proposed diagnostic tool will be implemented as a stopping criterion for the optimization algorithm known as simulated annealing, which finds the global maximum or minimum of a function through an iterative improvement approach.
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