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Note on neural network sampling for Bayesian inference of mixture processes

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

Abstract

In this paper we show some further experiments with neural network sampling, a class of sampling methods that make use of neural network approximations to (posterior) densities, introduced by Hoogerheide et al. (2007). We consider a method where a mixture of Student's t densities, which can be interpreted as a neural network function, is used as a candidate density in importance sampling or the Metropolis-Hastings algorithm. It is applied to an illustrative 2-regime mixture model for the US real GNP growth rate. We explain the non-elliptical shapes of the posterior distribution, and show that the proposed method outperforms Gibbs sampling with data augmentation and the griddy Gibbs sampler.

Suggested Citation

  • Hoogerheide, L.F. & van Dijk, H.K., 2007. "Note on neural network sampling for Bayesian inference of mixture processes," Econometric Institute Research Papers EI 2007-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:10090
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    References listed on IDEAS

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    1. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
    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, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
    4. Fruhwirth-Schnatter S., 2001. "Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 194-209, March.
    5. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    6. Bauwens, Luc & Bos, Charles S. & van Dijk, Herman K. & van Oest, Rutger D., 2004. "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," Journal of Econometrics, Elsevier, vol. 123(2), pages 201-225, December.
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