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Density estimation via Bayesian inference engines

Author

Listed:
  • M. P. Wand

    (University of Technology Sydney)

  • J. C. F. Yu

    (University of Technology Sydney)

Abstract

We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies demonstrate that the proposed density estimates have excellent comparative performance and scale well to very large sample sizes due to a binning strategy. Moreover, the approach is fully Bayesian and all estimates are accompanied by point-wise credible intervals. An accompanying package in the R language facilitates easy use of the new density estimates.

Suggested Citation

  • M. P. Wand & J. C. F. Yu, 2022. "Density estimation via Bayesian inference engines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 199-216, June.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00422-8
    DOI: 10.1007/s10182-021-00422-8
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    References listed on IDEAS

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    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    2. Hall, Peter & Titterington, D. M., 1988. "On confidence bands in nonparametric density estimation and regression," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 228-254, October.
    3. Hall, Peter & Wand, M. P., 1996. "On the Accuracy of Binned Kernel Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 165-184, February.
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