Overview of ABC

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

Handbook of Approximate Bayesian Computation

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

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-1

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Abstract

In Bayesian inference, complete knowledge about a vector of model parameters, θ ∈ Θ, obtained by fitting a model ℳ y o b s ∈ Y , is contained in the posterior distribution. Here, prior beliefs about the model parameters, as expressed through the prior distribution, π(θ), are updated by observing data π ( θ | y o b s ) = p ( y o b s | θ ) π ( θ ) ∫ Θ p ( y o b s | θ ) π ( θ )   d θ , through the likelihood function p(yobs |θ) of the model. Using Bayes’ theorem, the resulting posterior distribution: π ( θ | y o b s )   ≈   1 N ∑ i   =   1 N δ θ ( i )   ( θ ) ,

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