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Neural network approximations to posterior densities: an analytical approach

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  • Hoogerheide, L.F.
  • Kaashoek, J.F.
  • van Dijk, H.K.

Abstract

In Hoogerheide, Kaashoek and Van Dijk (2002) the class of neural network sampling methods is introduced to sample from a target (posterior) distribution that may be multi-modal or skew, or exhibit strong correlation among the parameters. In these methods the neural network is used as an importance function in IS or as a candidate density in MH. In this note we suggest an analytical approach to estimate the moments of a certain (target) distribution, where `analytical' refers to the fact that no sampling algorithm like MH or IS is needed.We show an example in which our analytical approach is feasible, even in a case where a `standard' Gibbs approach would fail or be extremely slow.

Suggested Citation

  • Hoogerheide, L.F. & Kaashoek, J.F. & van Dijk, H.K., 2003. "Neural network approximations to posterior densities: an analytical approach," Econometric Institute Research Papers EI 2003-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1047
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    3. Hoogerheide, L.F. & Kaashoek, J.F. & van Dijk, H.K., 2002. "Functional approximations to posterior densities: a neural network approach to efficient sampling," Econometric Institute Research Papers EI 2002-48, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. 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.
    5. van Dijk, H. K. & Kloek, T., 1980. "Further experience in Bayesian analysis using Monte Carlo integration," Journal of Econometrics, Elsevier, vol. 14(3), pages 307-328, December.
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    Cited by:

    1. Nalan Basturk & Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2012. "The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation," Tinbergen Institute Discussion Papers 12-096/III, Tinbergen Institute.
    2. Hoogerheide, L.F. & Kaashoek, J.F. & van Dijk, H.K., 2004. "Neural network based approximations to posterior densities: a class of flexible sampling methods with applications to reduced rank models," Econometric Institute Research Papers EI 2004-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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