Optimal scaling of mala for nonlinear regression

• 成果类型: Article
• 署名作者: Breyer, LA; Piccioni, M; Scarlatti, S
• 署名单位: Lancaster University; G d'Annunzio University of Chieti-Pescara; Sapienza University Rome
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000369
• 发表日期: 2004
• 页码: 1479-1505
• 关键词: Diffusions; metropolis

摘要

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.