Functional Approximations to Likelihoods/Posterior Densities: A Neural Network Approach to Efficient Sampling
AbstractThe 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
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 74.
Date of creation: 11 Aug 2004
Date of revision:
Markov chain Monte Carlo; importance sampling; neural networks; Bayesian inference;
Find related papers by JEL classification:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-08-16 (All new papers)
- NEP-CMP-2004-08-16 (Computational Economics)
- NEP-ECM-2004-08-16 (Econometrics)
- NEP-ETS-2004-08-16 (Econometric Time Series)
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