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A review of approximate Bayesian computation methods via density estimation: Inference for simulator‐models

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Yanan Fan, Clara Grazian

Published Online: Oct 29 2019

DOI: 10.1002/wics.1486

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Abstract This paper provides a review of approximate Bayesian computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional approaches. We show advantages and limitations of models based on parametric approaches and we then draw attention to developments in machine learning, which we believe have the potential to make ABC scalable to higher dimensions and may be the future direction for research in this area. This article is categorized under: Algorithms and Computational Methods < Algorithms Statistical and Graphical Methods of Data Analysis < Bayesian Methods and Theory Statistical Models < Simulation Models

Approximations of the posterior distributions for θ based on synthetic likelihood (left), standard approximate Bayesian computation (center) and Bayesian optimization for likelihood‐free inference (right) for the Gaussian example, with unknown location parameter and known variance. Solid line represents the true posterior distribution, dotted lines are the averages from 250 repetitions of the experiment, and the shaded area shows corresponding 95% pointwise variability intervals

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Approximations of the posterior distributions of log(r) based on synthetic likelihood (left), standard approximate Bayesian computation (center) and Bayesian optimization for likelihood‐free inference (right) for the Ricker model example. Top row obtained from 5 summary statistics, and bottom row 13 summary statistics. Solid vertical lines represents the true value, dotted lines are the averages from 250 repetitions of the experiment and the shaded areas show the 95% pointwise variability intervals

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An example of simulated data from the Ricker model with logr = 4, ϕ = 10, and σ = 0.3

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