Optimal scaling of MaLa for nonlinear regression

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. Methodol. 60 (1998) 255.268] for the i.i.d. case, showing the robustness of their analysis.