Adaptive proposal distribution for random walk Metropolis algorithm
Here, a new adaptive Markov Chain Monte Carlo method (MCMC) is introduced that yields a quick and flexible tool for estimating e.g. posteriori distributions in parameter estimation problems. Basically the method consists of the well-known Metropolis algorithm [see \textit{W.K. Hastings}, Biometrika 57, 97-109 (1970; Zbl 0219.65008)], where, however, the proposal distribution is tuned along the search according to the covariance calculated from a fixed number of previous states. This procedure makes sure that the MCMC process adapts to the target distribution, at least locally, and thus keeps the search effective all the time. The authors call this method Adaptive Proposal (AP). This paper is devoted to investigate the properties and practical usefulness of the AP algorithm. Although the stationary distribution of the AP algorithm is slightly biased, it appears to provide an efficient tool for, e.g., reasonable low-dimensional problems, as typically encountered in nonlinear regression problems in natural sciences. The AP algorithm is also applied in more realistic inverse problems applications. This problem arises in data processing of the Global Ozone Monitoring by Occultation of Stars satellite instruments. In this interesting application each analysis requires about 50 inversions. Moreover, when applying the Metropolis-Hastings method each inversion requires a quite individual proposal distribution. It appears that AP provides a valuable tool for this kind of applications.
scientific article; zbMATH DE number 1452444