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Local Kernel Dimension Reduction in Approximate Bayesian Computation

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Document pages: 18 pages

Abstract: Approximate Bayesian Computation (ABC) is a popular sampling method inapplications involving intractable likelihood functions. Instead of evaluatingthe likelihood function, ABC approximates the posterior distribution by a setof accepted samples which are simulated from a generating model. Simulatedsamples are accepted if the distances between the samples and the observation are smaller than somethreshold. The distance is calculated in terms of summary statistics. Thispaper proposes Local Gradient Kernel Dimension Reduction (LGKDR) to constructlow dimensional summary statistics for ABC. The proposed method identifies asufficient subspace of the original summary statistics by implicitlyconsidering all non-linear transforms therein, and a weighting kernel is usedfor the concentration of the projections. No strong assumptions are made on themarginal distributions, northe regression models, permitting usage in a wide range of applications.Experiments are done with simple rejection ABC and sequential Monte Carlo ABCmethods. Results are reported as competitive in the former and substantiallybetter in the latter cases in which Monte Carlo errors are compressed as muchas possible.

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