ABCD Inference
29 Pages Posted: 11 Feb 2013
Date Written: February 10, 2013
Abstract
In this paper we consider statistical inference using Approximate Bayesian Computation (ABC) and resolve two problems: The choice of summary statistics and the choice of constant in deciding whether synthetic and real data are close in a certain norm. We argue that the natural choice for summary statistics and the closeness norm is provided by the gradient of the log likelihood with respect to the parameters, the score vector (hence the D in the title of the paper). We apply the new techniques first in the context of general (possibly non-symmetric) stable Paretian distributions. The score vector is precomputed as a function of the parameters of the distribution (tail index and asymmetry) and it is approximated by using a nite Fourier expansion with respect to the argument. In empirical applications to Dow-Jones data we find that low-dimensional Fourier expansions of the score are sucient to deliver accurate approximations to the marginal posterior distributions. The new methods are applied also to a stochastic variance model using a modication of the score-based ABC technique which applies more generally to complex and intractable computer code models. We find that the results are quite encouraging and could enhance the applicability of ABC technology for generic models in a routine and highly ecient way.
Keywords: Bayesian analysis, Approximate Bayesian Computation, ABC, MCMC
JEL Classification: C11, C13
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