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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
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    1. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139, July.
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    7. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
    8. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
    9. Bauwens, L. & Bos, C.S. & van Dijk, H.K. & van Oest, R.D., 2002. "Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods," Econometric Institute Research Papers EI 2002-27, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Luc Bauwens & Charles S. Bos & Herman K. van Dijk & Rutger D. van Oest, 2002. "Adaptive Polar Sampling," Computing in Economics and Finance 2002 307, Society for Computational Economics.
    11. Richard Paap & Herman K. van Dijk, 1999. "Bayes Estimates of Markov Trends in possibly Cointegrated Series: An Application to US Consumption and Income," Tinbergen Institute Discussion Papers 99-024/4, Tinbergen Institute.
    12. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    13. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
    14. Rombouts, Jeroen V. K. & Bauwens, Luc, 2004. "Econometrics," Papers 2004,33, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
    15. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
    16. 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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