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Scalable Rejection Sampling for Bayesian Hierarchical Models

Author

Listed:
  • Michael Braun

    (Edwin L. Cox School of Business, Southern Methodist University, Dallas, Texas 75275)

  • Paul Damien

    (McCombs School of Business, University of Texas at Austin, Austin, Texas 78712)

Abstract

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from a large number of units. We develop a new method to sample from posterior distributions of Bayesian models, without using MCMC. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. The algorithm is scalable under the weak assumption that individual units are conditionally independent, making it applicable for large data sets. It can also be used to compute marginal likelihoods.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mksc.2014.0901 .

Suggested Citation

  • Michael Braun & Paul Damien, 2016. "Scalable Rejection Sampling for Bayesian Hierarchical Models," Marketing Science, INFORMS, vol. 35(3), pages 427-444, May.
    • Handle: RePEc:inm:ormksc:v:35:y:2016:i:3:p:427-444
    DOI: 10.1287/mksc.2014.0901
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    References listed on IDEAS

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    1. John D. C. Little, 1970. "Models and Managers: The Concept of a Decision Calculus," Management Science, INFORMS, vol. 16(8), pages 466-485, April.
    2. Peter E. Rossi & Greg M. Allenby, 2003. "Bayesian Statistics and Marketing," Marketing Science, INFORMS, vol. 22(3), pages 304-328, July.
    3. Bates, Douglas & Eddelbuettel, Dirk, 2013. "Fast and Elegant Numerical Linear Algebra Using the RcppEigen Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i05).
    4. Braun, Michael, 2014. "trustOptim: An R Package for Trust Region Optimization with Sparse Hessians," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i04).
    5. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    6. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
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    Cited by:

    1. Roozbeh Irani-Kermani & Edward C. Jaenicke & Ardalan Mirshani, 2023. "Accommodating heterogeneity in brand loyalty estimation: application to the U.S. beer retail market," Journal of Marketing Analytics, Palgrave Macmillan, vol. 11(4), pages 820-835, December.
    2. Pradeep Chintagunta & Dominique M. Hanssens & John R. Hauser, 2016. "Editorial—Marketing Science and Big Data," Marketing Science, INFORMS, vol. 35(3), pages 341-342, May.

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