Accelerating adaptation in the adaptive Metropolis–Hastings random walk algorithm

The Metropolis–Hastings random walk algorithm remains popular with practitioners due to the wide variety of situations in which it can be successfully applied and extreme ease implemented. Adaptive versions use information from early iterations Markov chain improve efficiency proposal. aim this paper is reduce number needed adapt proposal target, particularly important when likelihood time-consuming evaluate. First, accelerated shaping a generalisation both adaptive Metropolis algorithms. It designed remove, estimate covariance matrix misleading start chain. Second, scaling rapidly changes scale achieve target acceptance rate. usefulness these approaches illustrated range examples.