Optimal scaling of mala for nonlinear regression

Abstract

We address the problem of simulating efficiently from the posterior distribution over the parameters of a particular class of nonlinear regression models using a Langevin-Metropolis sampler. It is shown that as the number N of parameters increases, the proposal variance must scale as N -1/3 in order to converge to a diffusion. This generalizes previous results of Roberts and Rosenthal [J. R. Stat. Soc. Ser. B Stat. Mathodol. 60 (1998) 255-268] for the i.i.d. case, showing the robustness of their analysis. © Institute of Mathematical Statistics, 2004.