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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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