ABSTRACT
This chapter presents the toolbox and computational tools. It presents a review of traditional Markov chain Monte Carlo methodology, perfect sampling, and time inhomogeneous Markov chain Monte Carlo models. The chapter provides an extensive introduction to the Feynman-Kac particle methodology, by giving a unified treatment of a large set of models with different names and guises scattered around in a variety of application domains. It emphasizes that the weak ergodic theorem can be extended to any Markov chain which forgets its initial condition sufficiently fast. The chapter discusses the evolution of the simulated annealing in the context of the travelling salesman model. One idea is to introduce an intermediate acceptance-rejection mechanism every time the author changes the temperature parameter.
