Abstract
AbstractOver the past ten years, Approximate Bayesian Computation (ABC) has become hugely popular to estimate the parameters of a model when the likelihood function cannot be computed in a reasonable amount of time. ABC can in principle be used also to perform Bayesian model comparison, but this raises the question of which summary statistic should be used for such applications. Here we present a general method for constructing a summary statistic that is sufficient for the model choice problem. We apply this construction to models from the exponential family. Unfortunately, in more complex models, our construct often results in statistics with too high dimensionality to use in ABC. We therefore discuss the possibility of applying ABC with non-sufficient statistics.
Highlights
ABC in London Workshop Imperial College LondonPritchard et al (1999) proposed the ABC algorithm to approximately sample from p(θ|xobs): Slide 2 of 13
Proposed ABC approach to model selection when M1 nested in M2: infer under M2 with prior such that M1 gets half of the weight
If M1 and M2 are both nested in model M, any summary statistic sufficient for model M is sufficient for comparing M1 and M2
Summary
Pritchard et al (1999) proposed the ABC algorithm to approximately sample from p(θ|xobs): Slide 2 of 13. Proposed ABC approach to model selection when M1 nested in M2: infer under M2 with prior such that M1 gets half of the weight
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