Optimal Scaling of Mala for Nonlinear Regression

Details Optimal Scaling of Mala for Nonlinear Regression Optimal Scaling of Mala for Nonlinear Regression

2004-07-08

arxiv.org/abs/math/0407132v1

Annals of Probability 2004, Vol. 14, No. 3, 1479-1505

Mathematics

Probability

Scientific paper

10.1214/105051604000000369

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.

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