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A Primer on Bayesian Distributional Regression

Author

Listed:
  • Thomas Kneib
  • Nikolaus Umlauf
Abstract
Bayesian methods have become increasingly popular in the past two decades. With the constant rise of computational power even very complex models can be estimated on virtually any modern computer. Moreover, interest has shifted from conditional mean models to probabilistic distributional models capturing location, scale, shape and other aspects of a response distribution, where covariate effects can have flexible forms, e.g., linear, nonlinear, spatial or random effects. This tutorial paper discusses how to select models in the Bayesian distributional regression setting, how to monitor convergence of the Markov chains, evaluate relevance of effects using simultaneous credible intervals and how to use simulation-based inference also for quantities derived from the original model parameterisation. We exemplify the work flow using daily weather data on (i) temperatures on Germany's highest mountain and (ii) extreme values of precipitation all over Germany.

Suggested Citation

  • Thomas Kneib & Nikolaus Umlauf, 2017. "A Primer on Bayesian Distributional Regression," Working Papers 2017-13, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2017-13
    as

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    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2017-13.pdf
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    References listed on IDEAS

    as
    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    2. Nadja Klein & Thomas Kneib & Stefan Lang, 2015. "Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 405-419, March.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
    4. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    5. Nikolaus Umlauf & Nadja Klein & Achim Zeileis, 2017. "BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond)," Working Papers 2017-05, Faculty of Economics and Statistics, Universität Innsbruck.
    6. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    7. Nadja Klein & Thomas Kneib & Stephan Klasen & Stefan Lang, 2015. "Bayesian structured additive distributional regression for multivariate responses," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(4), pages 569-591, August.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    9. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    10. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    11. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Distributional regression; generalized additive models for location; scale and shape; Markov chain Monte Carlo simulations; semiparametric regression; tutorial;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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