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Optimal Auxiliary Priors And Reversible Jump Proposals For A Class Of Variable Dimension Models

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  • Norets, Andriy

Abstract

This article develops a Markov chain Monte Carlo (MCMC) method for a class of models that encompasses finite and countable mixtures of densities and mixtures of experts with a variable number of mixture components. The method is shown to maximize the expected probability of acceptance for cross-dimensional moves and to minimize the asymptotic variance of sample average estimators under certain restrictions. The method can be represented as a retrospective sampling algorithm with an optimal choice of auxiliary priors and as a reversible jump algorithm with optimal proposal distributions. The method is primarily motivated by and applied to a Bayesian nonparametric model for conditional densities based on mixtures of a variable number of experts. The mixture of experts model outperforms standard parametric and nonparametric alternatives in out of sample performance comparisons in an application to Engel curve estimation. The proposed MCMC algorithm makes estimation of this model practical.

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  • Norets, Andriy, 2021. "Optimal Auxiliary Priors And Reversible Jump Proposals For A Class Of Variable Dimension Models," Econometric Theory, Cambridge University Press, vol. 37(1), pages 49-81, February.
    • Handle: RePEc:cup:etheor:v:37:y:2021:i:1:p:49-81_2
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    Cited by:

    1. Norets, Andriy & Pelenis, Justinas, 2022. "Adaptive Bayesian estimation of conditional discrete-continuous distributions with an application to stock market trading activity," Journal of Econometrics, Elsevier, vol. 230(1), pages 62-82.
    2. Andriy Norets & Justinas Pelenis, 2022. "Adaptive Bayesian Estimation of Discrete‐Continuous Distributions Under Smoothness and Sparsity," Econometrica, Econometric Society, vol. 90(3), pages 1355-1377, May.

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