Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics...

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Bibliographic Details
Published in:arXiv.org 2009-02
Main Authors: Blum, M G B, Francois, O
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Bayesian analysis
Economic models
Importance sampling
Machine learning
Queues
Regression models
State of the art
Statistical analysis
Statistical inference
Statistics
Online Access:Get full text
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Summary:Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.
ISSN:2331-8422
DOI:10.48550/arxiv.0809.4178