Functional Approximations to Likelihoods/Posterior Densities: A Neural Network Approach to Efficient Sampling

Lennart F. Hoogerheide and Johan F. Kaashoek

No 74, Computing in Economics and Finance 2004 from Society for Computational Economics

Abstract: The performance of Monte Carlo integration methods like importance-sampling or Markov-Chain Monte-Carlo procedures depends greatly on the choice of the importance- or candidate-density. Such a density must typically be "close" to the target density to yield numerically accurate results with efficient sampling. Neural networks are natural importance- or candidate-densities since they have a universal approximation property and are easy to sample from. That is, conditional upon the specified neural network, sampling can be done either directly or using a Gibbs sampling technique, possibly with auxiliary variables. We propose such a class of methods, a key step for which is the construction of a neural network that approximates the target density accurately. The methods are tested on a set of illustrative models that includes a mixture of normal distributions, a Bayesian instrumental-variable regression problem with weak instruments and near-identification, and a two-regime growth model for US recessions and expansions. These examples involve experiments with non-standard, non-elliptical posterior distributions. The results indicate the feasibility of the neural network approach

Keywords: Markov chain Monte Carlo; importance sampling; neural networks; Bayesian inference (search for similar items in EconPapers)
JEL-codes: C11 C15 C45 (search for similar items in EconPapers)
Date: 2004-08-11
New Economics Papers: this item is included in nep-cmp, nep-ecm and nep-ets
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