On Adaptive Markov Chain Monte Carlo Algorithms
نویسندگان
چکیده
Abstract We look at adaptive MCMC algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the past of the process. We show under certain conditions that the generated stochastic process is ergodic, with appropriate stationary distribution. We then consider the Random Walk Metropolis (RWM) algorithm with normal proposal and scale parameter σ. We propose an adaptive version of this algorithm that sequentially adjusts σ using a Robbins-Monro type algorithm in order to nd the optimal scale parameter σopt as in Roberts et al. (1997). We show, under some additional conditions that this adaptive algorithm is ergodic and that σn, the sequence of scale parameter obtained converges almost surely to σopt. Our algorithm thus automatically determines and runs the optimal RWM scaling, with no manual tuning required. We close with a simulation example.
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