ABSTRACT Approximate Bayesian Computation (ABC) is a popular sampling method in
applications involving intractable likelihood functions. Instead of evaluating
the likelihood function, ABC approximates the posterior distribution by a set
of accepted samples which are simulated from a generating model. Simulated
samples are accepted if the distances between the samples and the observation are smaller than some
threshold. The distance is calculated in terms of summary statistics. This
paper proposes Local Gradient Kernel Dimension Reduction (LGKDR) to construct
low dimensional summary statistics for ABC. The proposed method identifies a
sufficient subspace of the original summary statistics by implicitly
considering all non-linear transforms therein, and a weighting kernel is used
for the concentration of the projections. No strong assumptions are made on the
marginal distributions, nor
the regression models, permitting usage in a wide range of applications.
Experiments are done with simple rejection ABC and sequential Monte Carlo ABC
methods. Results are reported as competitive in the former and substantially
better in the latter cases in which Monte Carlo errors are compressed as much
Cite this paper
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