ABC Samplers

Authored by: S. A. Sisson , Y. Fan

Handbook of Approximate Bayesian Computation

Print publication date:  August  2018
Online publication date:  August  2018

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-4

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Abstract

Approximate Bayesian computation (ABC) is a phrase that describes a collection of methods and algorithms designed to perform a Bayesian analysis using an approximation to the true posterior distribution, when the likelihood function implied by the data generating process is computationally intractable. For observed data π A B C   ( θ | s o b s )   ∝   ∫ K h   ( ‖ s   −   s o b s ‖ )   p   ( s | θ )   π   ( θ )   d s , , the likelihood function p(y|θ) depends on a vector of model parameters θ ∈ Θ, from which prior beliefs π(θ) may be updated into posterior beliefs π(θ|yobs ) ∝ p(yobs |θ)π(θ) via Bayes’ theorem. In the standard ABC framework (see e.g. Sisson et al. 2018, Chapter 1, this volume), the ABC approximation to π(θ|yobs ) is given by: 4.1 lim h → 0   π A B C   ( θ | s o b s )   ∝   ∫ δ s o b s   ( s ) p   ( s | θ )   π   ( θ )   d s   =   p   ( s o b s | θ )   π   ( θ )   ∝   π   ( θ | s o b s ) .

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