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August 2004 Optimal scaling of MaLa for nonlinear regression
Laird Arnault Breyer, Mauro Piccioni, Sergio Scarlatti
Ann. Appl. Probab. 14(3): 1479-1505 (August 2004). DOI: 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 N1/3 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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Laird Arnault Breyer. Mauro Piccioni. Sergio Scarlatti. "Optimal scaling of MaLa for nonlinear regression." Ann. Appl. Probab. 14 (3) 1479 - 1505, August 2004.


Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1048.62062
MathSciNet: MR2071431
Digital Object Identifier: 10.1214/105051604000000369

Primary: 60F17
Secondary: 60F05 , 60F10

Keywords: Bayesian nonlinear regression , Hastings–Metropolis , Langevin diffusion , Markov chain Monte Carlo , propagation of chaos

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 3 • August 2004
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