(ε− α)−MCMC-Approximation under Drift Condition

An essential part of many problems encountered in Bayesian inference is the computation of analytically intractable integral I = πf = ∫ X f(x)π(x)dx, where f(x) is the target function of interest, X is often a region in high-dimensional space and the probability distribution π over X is usually known up to a normalizing constant and direct simulation from π is not feasible. The classical MCMC approach to this problem is to generate an ergodic Markov chain (Xn)n≥0, using a transition kernel P , with stationary distribution π, which ensures convergence of L(Xn) to π and then estimate I by averages along a single trajectory i.e. by taking