Two-Stage Metropolis-Hastings for Tall Data

This paper discusses the challenges presented by tall data problems associated with Bayesian classification (specifically binary classification) and the existing methods to handle them. Current methods include parallelizing the likelihood, subsampling, and consensus Monte Carlo. A new method based o...

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Bibliographic Details
Published in:Journal of classification 2018-04, Vol.35 (1), p.29-51
Main Authors: Payne, Richard D., Mallick, Bani K.
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Bioinformatics
Classification
Computer simulation
Marketing
Mathematics and Statistics
Monte Carlo simulation
Parallel processing
Pattern Recognition
Psychometrics
Regression
Signal,Image and Speech Processing
Splines
Statistical Theory and Methods
Statistics
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Summary:This paper discusses the challenges presented by tall data problems associated with Bayesian classification (specifically binary classification) and the existing methods to handle them. Current methods include parallelizing the likelihood, subsampling, and consensus Monte Carlo. A new method based on the two-stage Metropolis-Hastings algorithm is also proposed. The purpose of this algorithm is to reduce the exact likelihood computational cost in the tall data situation. In the first stage, a new proposal is tested by the approximate likelihood based model. The full likelihood based posterior computation will be conducted only if the proposal passes the first stage screening. Furthermore, this method can be adopted into the consensus Monte Carlo framework. The two-stage method is applied to logistic regression, hierarchical logistic regression, and Bayesian multivariate adaptive regression splines.
ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-018-9248-z