IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v27y2022i2d10.1007_s13253-021-00485-9.html
   My bibliography  Save this article

Greater Than the Sum of its Parts: Computationally Flexible Bayesian Hierarchical Modeling

Author

Listed:
  • Devin S. Johnson

    (National Marine Fisheries Service, NOAA)

  • Brian M. Brost

    (National Marine Fisheries Service, NOAA)

  • Mevin B. Hooten

    (The University of Texas at Austin)

Abstract

We propose a multistage method for making inference at all levels of a Bayesian hierarchical model (BHM) using natural data partitions to increase efficiency by allowing computations to take place in parallel form using software that is most appropriate for each data partition. The full hierarchical model is then approximated by the product of independent normal distributions for the data component of the model. In the second stage, the Bayesian maximum a posteriori (MAP) estimator is found by maximizing the approximated posterior density with respect to the parameters. If the parameters of the model can be represented as normally distributed random effects, then the second-stage optimization is equivalent to fitting a multivariate normal linear mixed model. We consider a third stage that updates the estimates of distinct parameters for each data partition based on the results of the second stage. The method is demonstrated with two ecological data sets and models, a generalized linear mixed effects model (GLMM) and an integrated population model (IPM). The multistage results were compared to estimates from models fit in single stages to the entire data set. In both cases, multistage results were very similar to a full MCMC analysis. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Devin S. Johnson & Brian M. Brost & Mevin B. Hooten, 2022. "Greater Than the Sum of its Parts: Computationally Flexible Bayesian Hierarchical Modeling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 382-400, June.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:2:d:10.1007_s13253-021-00485-9
    DOI: 10.1007/s13253-021-00485-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-021-00485-9
    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/s13253-021-00485-9?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. P. Besbeas & B.J.T. Morgan, 2019. "Exact inference for integrated population modelling," Biometrics, The International Biometric Society, vol. 75(2), pages 475-484, June.
    2. Julian P. T. Higgins & Simon G. Thompson & David J. Spiegelhalter, 2009. "A re‐evaluation of random‐effects meta‐analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 137-159, January.
    3. Mevin B. Hooten & Frances E. Buderman & Brian M. Brost & Ephraim M. Hanks & Jacob S. Ivan, 2016. "Hierarchical animal movement models for population‐level inference," Environmetrics, John Wiley & Sons, Ltd., vol. 27(6), pages 322-333, September.
    4. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    5. Mevin B. Hooten & Devin S. Johnson & Brian M. Brost, 2021. "Making Recursive Bayesian Inference Accessible," The American Statistician, Taylor & Francis Journals, vol. 75(2), pages 185-194, May.
    6. Kristensen, Kasper & Nielsen, Anders & Berg, Casper W. & Skaug, Hans & Bell, Bradley M., 2016. "TMB: Automatic Differentiation and Laplace Approximation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i05).
    7. David Lunn & Jessica Barrett & Michael Sweeting & Simon Thompson, 2013. "Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 551-572, August.
    8. P. Besbeas & S. N. Freeman & B. J. T. Morgan & E. A. Catchpole, 2002. "Integrating Mark–Recapture–Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters," Biometrics, The International Biometric Society, vol. 58(3), pages 540-547, September.
    9. Skaug, Hans J. & Fournier, David A., 2006. "Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 699-709, November.
    10. Christopher K. Wikle, 2003. "Hierarchical Models in Environmental Science," International Statistical Review, International Statistical Institute, vol. 71(2), pages 181-199, August.
    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. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    2. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    3. Ben C. Stevenson & Rachel M. Fewster & Koustubh Sharma, 2022. "Spatial correlation structures for detections of individuals in spatial capture–recapture models," Biometrics, The International Biometric Society, vol. 78(3), pages 963-973, September.
    4. Dennis, Emily B. & Kéry, Marc & Morgan, Byron J.T. & Coray, Armin & Schaub, Michael & Baur, Bruno, 2021. "Integrated modelling of insect population dynamics at two temporal scales," Ecological Modelling, Elsevier, vol. 441(C).
    5. David L. Miller & Richard Glennie & Andrew E. Seaton, 2020. "Understanding the Stochastic Partial Differential Equation Approach to Smoothing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 1-16, March.
    6. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.
    7. Roland Langrock & Timo Adam & Vianey Leos‐Barajas & Sina Mews & David L. Miller & Yannis P. Papastamatiou, 2018. "Spline‐based nonparametric inference in general state‐switching models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 179-200, August.
    8. Besbeas, P.T. & McCrea, R.S. & Morgan, B.J.T., 2022. "Selecting age structure in integrated population models," Ecological Modelling, Elsevier, vol. 473(C).
    9. Ingrid Sandvig Thorsen & Bård Støve & Hans J. Skaug, 2023. "A TMB Approach to Study Spatial Variation in Weather-Generated Claims in Insurance," SN Operations Research Forum, Springer, vol. 4(4), pages 1-27, December.
    10. William H. Aeberhard & Eva Cantoni & Chris Field & Hans R. Künsch & Joanna Mills Flemming & Ximing Xu, 2021. "Robust estimation for discrete‐time state space models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1127-1147, December.
    11. Byron J. T. Morgan, 2022. "M. Schaub and M. Kéry: Integrated Population Models Theory and Ecological Applications with R and JAGS, Academic Press, 2022," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 595-597, December.
    12. Zheng, Nan & Cadigan, Noel, 2021. "Frequentist delta-variance approximations with mixed-effects models and TMB," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    13. Ruggero Bellio & Nicola Soriani, 2021. "Maximum likelihood estimation based on the Laplace approximation for p2 network regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 24-41, February.
    14. Cole C Monnahan & Kasper Kristensen, 2018. "No-U-turn sampling for fast Bayesian inference in ADMB and TMB: Introducing the adnuts and tmbstan R packages," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-10, May.
    15. Gerhard Tutz & Moritz Berger, 2018. "Tree-structured modelling of categorical predictors in generalized additive regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 737-758, September.
    16. Katherine Wilson & Jon Wakefield, 2022. "A probabilistic model for analyzing summary birth history data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(11), pages 291-344.
    17. Tommaso Luzzati & Angela Parenti & Tommaso Rughi, 2017. "Spatial error regressions for testing the Cancer-EKC," Discussion Papers 2017/218, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    18. Yeojin Chung & Sophia Rabe-Hesketh & Vincent Dorie & Andrew Gelman & Jingchen Liu, 2013. "A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 685-709, October.
    19. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    20. Sofia Dias & Alex J. Sutton & Nicky J. Welton & A. E. Ades, 2013. "Evidence Synthesis for Decision Making 3," Medical Decision Making, , vol. 33(5), pages 618-640, July.

    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:jagbes:v:27:y:2022:i:2:d:10.1007_s13253-021-00485-9. 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.