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Moment conditions and Bayesian non‐parametrics

Author

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  • Luke Bornn
  • Neil Shephard
  • Reza Solgi

Abstract

Models phrased through moment conditions are central to much of modern inference. Here these moment conditions are embedded within a non‐parametric Bayesian set‐up. Handling such a model is not probabilistically straightforward as the posterior has support on a manifold. We solve the relevant issues, building new probability and computational tools by using Hausdorff measures to analyse them on real and simulated data. These new methods, which involve simulating on a manifold, can be applied widely, including providing Bayesian analysis of quasi‐likelihoods, linear and non‐linear regression, missing data and hierarchical models.

Suggested Citation

  • Luke Bornn & Neil Shephard & Reza Solgi, 2019. "Moment conditions and Bayesian non‐parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(1), pages 5-43, February.
    • Handle: RePEc:bla:jorssb:v:81:y:2019:i:1:p:5-43
    DOI: 10.1111/rssb.12294
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    Cited by:

    1. Yusuke Narita & Kohei Yata, 2021. "Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules," Working Papers 2021-022, Human Capital and Economic Opportunity Working Group.
    2. Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    3. Luo, Yu & Graham, Daniel J. & McCoy, Emma J., 2023. "Semiparametric Bayesian doubly robust causal estimation," LSE Research Online Documents on Economics 117944, London School of Economics and Political Science, LSE Library.
    4. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    5. Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.

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