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

  • Lennart F. Hoogerheide
  • Johan F. Kaashoek
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    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

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    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 74.

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    Date of creation: 11 Aug 2004
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    Handle: RePEc:sce:scecf4:74
    Contact details of provider: Web page: http://comp-econ.org/
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    1. BAUWENS, Luc & ROMBOUTS, Jeroen V.K., . "Econometrics," CORE Discussion Papers RP 1713, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Rombouts, Jeroen V. K. & Bauwens, Luc, 2004. "Econometrics," Papers 2004,33, Humboldt-Universit√§t Berlin, Center for Applied Statistics and Economics (CASE).
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    6. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
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    10. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
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    16. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
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