IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v106y2022i2d10.1007_s10182-021-00422-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-021-00422-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-021-00422-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    2. Francis,David C. & Kubinec ,Robert, 2022. "Beyond Political Connections : A Measurement Model Approach to Estimating Firm-levelPolitical Influence in 41 Economies," Policy Research Working Paper Series 10119, The World Bank.
    3. Martinovici, A., 2019. "Revealing attention - how eye movements predict brand choice and moment of choice," Other publications TiSEM 7dca38a5-9f78-4aee-bd81-c, Tilburg University, School of Economics and Management.
    4. Yongping Bao & Ludwig Danwitz & Fabian Dvorak & Sebastian Fehrler & Lars Hornuf & Hsuan Yu Lin & Bettina von Helversen, 2022. "Similarity and Consistency in Algorithm-Guided Exploration," CESifo Working Paper Series 10188, CESifo.
    5. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    6. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," Papers 2012.14503, arXiv.org.
    7. van Kesteren Erik-Jan & Bergkamp Tom, 2023. "Bayesian analysis of Formula One race results: disentangling driver skill and constructor advantage," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 19(4), pages 273-293, December.
    8. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    9. Holmström, Lasse, 2000. "The Accuracy and the Computational Complexity of a Multivariate Binned Kernel Density Estimator," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 264-309, February.
    10. Xiaoyue Xi & Simon E. F. Spencer & Matthew Hall & M. Kate Grabowski & Joseph Kagaayi & Oliver Ratmann & Rakai Health Sciences Program and PANGEA‐HIV, 2022. "Inferring the sources of HIV infection in Africa from deep‐sequence data with semi‐parametric Bayesian Poisson flow models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 517-540, June.
    11. Kuschnig, Nikolas, 2021. "Bayesian Spatial Econometrics and the Need for Software," Department of Economics Working Paper Series 318, WU Vienna University of Economics and Business.
    12. Deniz Aksoy & David Carlson, 2022. "Electoral support and militants’ targeting strategies," Journal of Peace Research, Peace Research Institute Oslo, vol. 59(2), pages 229-241, March.
    13. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    14. D. Fouskakis & G. Petrakos & I. Rotous, 2020. "A Bayesian longitudinal model for quantifying students’ preferences regarding teaching quality indicators," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 255-270, August.
    15. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    16. Joseph B. Bak-Coleman & Ian Kennedy & Morgan Wack & Andrew Beers & Joseph S. Schafer & Emma S. Spiro & Kate Starbird & Jevin D. West, 2022. "Combining interventions to reduce the spread of viral misinformation," Nature Human Behaviour, Nature, vol. 6(10), pages 1372-1380, October.
    17. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    18. Jonas Moss & Riccardo De Bin, 2023. "Modelling publication bias and p‐hacking," Biometrics, The International Biometric Society, vol. 79(1), pages 319-331, March.
    19. 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.
    20. David M. Phillippo & Sofia Dias & A. E. Ades & Mark Belger & Alan Brnabic & Alexander Schacht & Daniel Saure & Zbigniew Kadziola & Nicky J. Welton, 2020. "Multilevel network meta‐regression for population‐adjusted treatment comparisons," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1189-1210, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00422-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.