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m link Jonathan K. Pritchard |
Eclecticos (talk | contribs) →Overview: minor clarification |
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The explicit evaluation of the likelihood <math>P(D|\theta)</math> is avoided in ABC approaches by considering distances between observed and data simulated from a model with parameter <math>\theta</math>. For sufficiently complex models and large data sets the probability of happening upon a simulation run that yields precisely the same dataset as the one observed will be very small, often unacceptably so. So rather than considering the data we consider a summary statistic of the data, <math>S(D)</math>, and use a distance <math>\Delta(S(D),S(X))</math> between the summary statistics of real and simulated data, <math>D</math> and <math>X</math>, respectively.
The generic ABC approach to infer the posterior probability distribution of a parameter <math>\theta</math> is as follows:
:# Sample a candidate parameter vector <math>\theta^\ast</math> from some proposal distribution <math>\pi(\theta)</math>.
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