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.
Publié le : 2004-08-14
Classification:
Bayesian nonlinear regression,
Markov chain Monte Carlo,
Hastings–Metropolis,
Langevin diffusion,
propagation of chaos,
60F17,
60F05,
60F10
@article{1089736293,
author = {Breyer, Laird Arnault and Piccioni, Mauro and Scarlatti, Sergio},
title = {Optimal scaling of MaLa for nonlinear regression},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 1479-1505},
language = {en},
url = {http://dml.mathdoc.fr/item/1089736293}
}
Breyer, Laird Arnault; Piccioni, Mauro; Scarlatti, Sergio. Optimal scaling of MaLa for nonlinear regression. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 1479-1505. http://gdmltest.u-ga.fr/item/1089736293/