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2015 ; 25
(2
): 289-301
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Piecewise Approximate Bayesian Computation: fast inference for discretely
observed Markov models using a factorised posterior distribution
#MMPMID26097293
White SR
; Kypraios T
; Preston SP
Stat Comput
2015[]; 25
(2
): 289-301
PMID26097293
show ga
Many modern statistical applications involve inference for complicated stochastic
models for which the likelihood function is difficult or even impossible to
calculate, and hence conventional likelihood-based inferential techniques cannot
be used. In such settings, Bayesian inference can be performed using Approximate
Bayesian Computation (ABC). However, in spite of many recent developments to ABC
methodology, in many applications the computational cost of ABC necessitates the
choice of summary statistics and tolerances that can potentially severely bias
the estimate of the posterior. We propose a new "piecewise" ABC approach suitable
for discretely observed Markov models that involves writing the posterior density
of the parameters as a product of factors, each a function of only a subset of
the data, and then using ABC within each factor. The approach has the advantage
of side-stepping the need to choose a summary statistic and it enables a
stringent tolerance to be set, making the posterior "less approximate". We
investigate two methods for estimating the posterior density based on ABC samples
for each of the factors: the first is to use a Gaussian approximation for each
factor, and the second is to use a kernel density estimate. Both methods have
their merits. The Gaussian approximation is simple, fast, and probably adequate
for many applications. On the other hand, using instead a kernel density estimate
has the benefit of consistently estimating the true piecewise ABC posterior as
the number of ABC samples tends to infinity. We illustrate the piecewise ABC
approach with four examples; in each case, the approach offers fast and accurate
inference.