[R-sig-ME] priors in multilevel modeling

Poe, John jdpo223 at g.uky.edu
Fri Mar 2 16:24:39 CET 2018

Hello everyone,

I'm doing an independent study with a student on advanced topics in
multilevel modeling and we are going to be hitting Bayesian multilevel
modeling before long. I'm looking for papers that either make specific
recommendations for prior and hyperprior choices in Bayesian multilevel
models or that compare the effects of different types of priors. Note that
this isn't for a specific application. I'm just trying to put together a
comprehensive reading list that goes through the types of things you can do
with priors in multilevel models and the consequences and benefits of
certain kinds of priors.

Any additional suggestions, critiques, or general insights on this topic
are *extremely* welcome.

These are what I've already got for those interested

On general prior construction:

   - Gelman, A., et al. (2017). "The prior can often only be understood in
   the context of the likelihood." Entropy 19(10): 555.
   - Kass, R. E. and L. Wasserman (1996). "The selection of prior
   distributions by formal rules." Journal of the American Statistical
   Association 91(435): 1343-1370.
   - Savage, Jim (2017) Your model gives you a lot of information about
   what your prior should(n’t) be. Blog Pos
   - McElreath, R. (2015). Big Entropy and the Generalized Linear Model.
   Statistical Rethinking, CRC Press.
   - Simpson, D., et al. (2017). "Penalising model component complexity: A
   principled, practical approach to constructing priors." Statistical Science
   32(1): 1-28.
   - Lopes, H. F. and J. L. Tobias (2011). "Confronting prior convictions:
   On issues of prior sensitivity and likelihood robustness in Bayesian
   analysis." Annu. Rev. Econ. 3(1): 107-131.
   - Betancourt, M. (2017) How the Shape of a Weakly Informative Prior
   Affects Inferences
   - Seaman III, J. W., et al. (2012). "Hidden dangers of specifying
   noninformative priors." The American Statistician 66(2): 77-84.

On priors in multilevel models

   - Browne, W. J. and D. Draper (2006). “A comparison of Bayesian and
   likelihood-based methods for fitting multilevel models.” Bayesian analysis
   1(3): 473-514.
   - Gelman, A. (2006). "Prior distributions for variance parameters in
   hierarchical models (comment on article by Browne and Draper)." Bayesian
   analysis 1(3): 515-534.
   - Kass, R. E. and R. Natarajan (2006). "A default conjugate prior for
   variance components in generalized linear mixed models (comment on article
   by Browne and Draper)." Bayesian analysis 1(3): 535-542.
   - Lambert, P. C. (2006). "Comment on article by Browne and Draper."
   Bayesian analysis 1(3): 543-546.
   - Browne, W. J. and D. Draper (2006). "Rejoinder." Bayesian analysis
   1(3): 547 - 550.
   - Congdon, P. D. (2010). Applied Bayesian hierarchical methods, CRC
   Press. Various chapters
   - Sun, D., et al. (2001). "Propriety of posteriors with improper priors
   in hierarchical linear mixed models." Statistica Sinica: 77-95.
   - Chung, Y., et al. (2015). "Weakly informative prior for point
   estimation of covariance matrices in hierarchical models." Journal of
   Educational and Behavioral Statistics 40(2): 136-157.
   - Piironen, J. and A. Vehtari (2016). "On the hyperprior choice for the
   global shrinkage parameter in the horseshoe prior." arXiv preprint
   - Hobert, J. P. and G. Casella (1996). "The effect of improper priors on
   Gibbs sampling in hierarchical linear mixed models." Journal of the
   American Statistical Association 91(436): 1461-1473.



John Poe, Ph.D.
Postdoctoral Scholar / Research Methodologist
Center for Public Health Services & Systems Research
University of Kentucky


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