Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

In this paper, we develop a Genetic Algorithm that can address the fundamental problem of how one should weight the summary statistics included in an approximate Bayesian computation analysis built around an accept/reject algorithm, and how one might choose the tolerance for that analysis. We then demonstrate that using weighted statistics, and a well-chosen tolerance, in such an approximate Bayesian computation approach can result in improved performance, when compared to unweighted analyses, using one example drawn purely from statistics and two drawn from the estimation of population genetics parameters.

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Graph metrics as summary statistics for Approximate Bayesian Computation with application to network model parameter estimation

Journal of Complex Networks ◽

10.1093/comnet/cnu009 ◽

2014 ◽

Vol 3 (1) ◽

pp. 52-83 ◽

Cited By ~ 6

Author(s):

D. Fay ◽

A. W. Moore ◽

K. Brown ◽

M. Filosi ◽

G. Jurman

Keyword(s):

Parameter Estimation ◽

Network Model ◽

Approximate Bayesian Computation ◽

Bayesian Computation ◽

Summary Statistics ◽

Model Parameter ◽

Model Parameter Estimation ◽

Graph Metrics ◽

Approximate Bayesian

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Choosing summary statistics by least angle regression for approximate Bayesian computation

Journal of Applied Statistics ◽

10.1080/02664763.2015.1134447 ◽

2016 ◽

Vol 43 (12) ◽

pp. 2191-2202 ◽

Cited By ~ 1

Author(s):

Muhammad Faisal ◽

Andreas Futschik ◽

Ijaz Hussain ◽

Mitwali Abd-el.Moemen

Keyword(s):

Approximate Bayesian Computation ◽

Bayesian Computation ◽

Summary Statistics ◽

Least Angle Regression ◽

Approximate Bayesian

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Component-wise Approximate Bayesian Computation via Gibbs-like steps

Biometrika ◽

10.1093/biomet/asaa090 ◽

2020 ◽

Author(s):

Grégoire Clarté ◽

Christian P Robert ◽

Robin J Ryder ◽

Julien Stoehr

Keyword(s):

Markov Chain ◽

Posterior Distribution ◽

Approximate Bayesian Computation ◽

Generative Models ◽

Bayesian Computation ◽

Summary Statistics ◽

Posterior Distributions ◽

Reduced Dimensions ◽

Standard Solution ◽

Approximate Bayesian

Abstract Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty, we explore a Gibbs version of the Approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.

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Choosing the Summary Statistics and the Acceptance Rate in Approximate Bayesian Computation

Proceedings of COMPSTAT'2010 ◽

10.1007/978-3-7908-2604-3_4 ◽

2010 ◽

pp. 47-56 ◽

Cited By ~ 11

Author(s):

Michael G.B. Blum

Keyword(s):

Approximate Bayesian Computation ◽

Acceptance Rate ◽

Bayesian Computation ◽

Summary Statistics ◽

Approximate Bayesian

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Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy

Algorithms ◽

10.3390/a13100265 ◽

2020 ◽

Vol 13 (10) ◽

pp. 265

Author(s):

Tom Burr ◽

Andrea Favalli ◽

Marcie Lombardi ◽

Jacob Stinnett

Keyword(s):

Approximate Bayesian Computation ◽

Gamma Ray ◽

Bayesian Computation ◽

Summary Statistics ◽

Area Estimation ◽

Estimation Algorithms ◽

Gamma Ray Spectroscopy ◽

Peak Location ◽

Approximate Bayesian ◽

Energy Channels

Radioisotope identification (RIID) algorithms for gamma-ray spectroscopy aim to infer what isotopes are present and in what amounts in test items. RIID algorithms either use all energy channels in the analysis region or only energy channels in and near identified peaks. Because many RIID algorithms rely on locating peaks and estimating each peak’s net area, peak location and peak area estimation algorithms continue to be developed for gamma-ray spectroscopy. This paper shows that approximate Bayesian computation (ABC) can be effective for peak location and area estimation. Algorithms to locate peaks can be applied to raw or smoothed data, and among several smoothing options, the iterative bias reduction algorithm (IBR) is recommended; the use of IBR with ABC is shown to potentially reduce uncertainty in peak location estimation. Extracted peak locations and areas can then be used as summary statistics in a new ABC-based RIID. ABC allows for easy experimentation with candidate summary statistics such as goodness-of-fit scores and peak areas that are extracted from relatively high dimensional gamma spectra with photopeaks (1024 or more energy channels) consisting of count rates versus energy for a large number of gamma energies.

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