IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v180y2023ics0167947322002389.html
   My bibliography  Save this article

BART-based inference for Poisson processes

Author

Listed:
  • Lamprinakou, Stamatina
  • Barahona, Mauricio
  • Flaxman, Seth
  • Filippi, Sarah
  • Gandy, Axel
  • McCoy, Emma J.

Abstract

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson processes is introduced. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. The new approach enables full posterior inference of the intensity in a non-parametric regression setting. The performance of the novel scheme is demonstrated through simulation studies on synthetic and real datasets up to five dimensions, and the new scheme is compared with alternative approaches.

Suggested Citation

  • Lamprinakou, Stamatina & Barahona, Mauricio & Flaxman, Seth & Filippi, Sarah & Gandy, Axel & McCoy, Emma J., 2023. "BART-based inference for Poisson processes," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002389
    DOI: 10.1016/j.csda.2022.107658
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002389
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107658?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. Sardy, Sylvain & Tseng, Paul, 2004. "On the Statistical Analysis of Smoothing by Maximizing Dirty Markov Random Field Posterior Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 191-204, January.
    2. P. A. W Lewis & G. S. Shedler, 1979. "Simulation of nonhomogeneous poisson processes by thinning," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 403-413, September.
    3. Antonio R. Linero, 2018. "Bayesian Regression Trees for High-Dimensional Prediction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 626-636, April.
    4. Zhang, Junni L. & Härdle, Wolfgang K., 2010. "The Bayesian Additive Classification Tree applied to credit risk modelling," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1197-1205, May.
    5. Kapelner, Adam & Bleich, Justin, 2016. "bartMachine: Machine Learning with Bayesian Additive Regression Trees," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i04).
    6. Peng, Roger, 2003. "Multi-dimensional Point Process Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i16).
    7. Antonio R. Linero & Yun Yang, 2018. "Bayesian regression tree ensembles that adapt to smoothness and sparsity," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 1087-1110, November.
    8. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
    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. Falco J. Bargagli Stoffi & Kenneth De Beckker & Joana E. Maldonado & Kristof De Witte, 2021. "Assessing Sensitivity of Machine Learning Predictions.A Novel Toolbox with an Application to Financial Literacy," Papers 2102.04382, arXiv.org.
    2. Falco J. Bargagli-Stoffi & Fabio Incerti & Massimo Riccaboni & Armando Rungi, 2023. "Machine Learning for Zombie Hunting: Predicting Distress from Firms' Accounts and Missing Values," Papers 2306.08165, arXiv.org.
    3. Yaojun Zhang & Lanpeng Ji & Georgios Aivaliotis & Charles Taylor, 2023. "Bayesian CART models for insurance claims frequency," Papers 2303.01923, arXiv.org, revised Dec 2023.
    4. Oyebayo Ridwan Olaniran & Ali Rashash R. Alzahrani, 2023. "On the Oracle Properties of Bayesian Random Forest for Sparse High-Dimensional Gaussian Regression," Mathematics, MDPI, vol. 11(24), pages 1-29, December.
    5. repec:jss:jstsof:35:i08 is not listed on IDEAS
    6. Jan Kluge & Sarah Lappöhn & Kerstin Plank, 2023. "Predictors of TFP growth in European countries," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 50(1), pages 109-140, February.
    7. Arii, Ken & Caspersen, John P. & Jones, Trevor A. & Thomas, Sean C., 2008. "A selection harvesting algorithm for use in spatially explicit individual-based forest simulation models," Ecological Modelling, Elsevier, vol. 211(3), pages 251-266.
    8. Jiao Jieying & Hu Guanyu & Yan Jun, 2021. "A Bayesian marked spatial point processes model for basketball shot chart," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 77-90, June.
    9. Frank Davenport, 2017. "Estimating standard errors in spatial panel models with time varying spatial correlation," Papers in Regional Science, Wiley Blackwell, vol. 96, pages 155-177, March.
    10. Leandro, Camila & Jay-Robert, Pierre & Mériguet, Bruno & Houard, Xavier & Renner, Ian W., 2020. "Is my sdm good enough? insights from a citizen science dataset in a point process modeling framework," Ecological Modelling, Elsevier, vol. 438(C).
    11. Jie Chen & Joseph Glaz, 2016. "Multiple Window Scan Statistics for Two Dimensional Poisson Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 967-977, December.
    12. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    13. Pierdzioch, Christian & Risse, Marian & Rohloff, Sebastian, 2016. "Are precious metals a hedge against exchange-rate movements? An empirical exploration using bayesian additive regression trees," The North American Journal of Economics and Finance, Elsevier, vol. 38(C), pages 27-38.
    14. Mohammadi, M. & Rezakhah, S. & Modarresi, N., 2020. "Semi-Lévy driven continuous-time GARCH process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    15. Chavez-Demoulin, V. & Embrechts, P. & Sardy, S., 2014. "Extreme-quantile tracking for financial time series," Journal of Econometrics, Elsevier, vol. 181(1), pages 44-52.
    16. Canyakmaz, Caner & Özekici, Süleyman & Karaesmen, Fikri, 2019. "An inventory model where customer demand is dependent on a stochastic price process," International Journal of Production Economics, Elsevier, vol. 212(C), pages 139-152.
    17. Wolfgang Karl Härdle & Dedy Dwi Prastyo, 2013. "Default Risk Calculation based on Predictor Selection for the Southeast Asian Industry," SFB 649 Discussion Papers SFB649DP2013-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    18. Martin Huber & David Imhof & Rieko Ishii, 2022. "Transnational machine learning with screens for flagging bid‐rigging cartels," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1074-1114, July.
    19. Vijay Rajagopal & Gregory Bass & Cameron G Walker & David J Crossman & Amorita Petzer & Anthony Hickey & Ivo Siekmann & Masahiko Hoshijima & Mark H Ellisman & Edmund J Crampin & Christian Soeller, 2015. "Examination of the Effects of Heterogeneous Organization of RyR Clusters, Myofibrils and Mitochondria on Ca2+ Release Patterns in Cardiomyocytes," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-31, September.
    20. Christoph Lambio & Tillman Schmitz & Richard Elson & Jeffrey Butler & Alexandra Roth & Silke Feller & Nicolai Savaskan & Tobia Lakes, 2023. "Exploring the Spatial Relative Risk of COVID-19 in Berlin-Neukölln," IJERPH, MDPI, vol. 20(10), pages 1-22, May.
    21. Liao, Jinbao & Li, Zhenqing & Quets, Jan J. & Nijs, Ivan, 2013. "Effects of space partitioning in a plant species diversity model," Ecological Modelling, Elsevier, vol. 251(C), pages 271-278.

    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:eee:csdana:v:180:y:2023:i:c:s0167947322002389. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.