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.
"Optimal scaling of MaLa for nonlinear regression." Ann. Appl. Probab. 14 (3) 1479 - 1505, August 2004. https://doi.org/10.1214/105051604000000369