Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/79279
Authors: 
Belloni, Alexandre
Chernozhukov, Victor
Year of Publication: 
2007
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP12/07
Abstract: 
In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using this observation, we establish polynomial bounds on the computational complexity of general Metropolis random walks methods in large samples. Our analysis covers cases, where the underlying log-likelihood or extremum criterion function is possibly nonconcave, discontinuous, and of increasing dimension. However, the central limit theorem restricts the deviations from continuity and log-concavity of the log-likelihood or extremum criterion function in a very specific manner.
Subjects: 
Monte Carlo , Computational Complexity , Curved Exponential
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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