Abstract
The standard Bayesian model is defined in terms of an outcome model and the prior density of the parameters. The latter depends on parameters called hyperparameters. A hierarchical Bayes model results when one or more of the hyperparameters are assumed to be random and modelled probabilistically. We discuss canonical versions of these models for the case when both the parameters and the hyperparameters are modelled in groups or blocks, provide relevant examples, and discuss how inference by Markov chain Monte Carlo methods makes even the fitting of complex hierarchical models practical and simple. The problem of model comparisons is also addressed.
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Bibliography
Albert, J.H., and S. Chib. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88: 669–679.
Berger, J. 1985. Statistical decision theory and Bayesian analysis. New York: Springer.
Chib, S. 1995. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90: 1313–1321.
Chib, S., and B.P. Carlin. 1999. On MCMC sampling in hierarchical longitudinal models. Statistics and Computing 9: 17–26.
Chib, S., and E. Greenberg. 1995. Understanding the metropolis-Hastings algorithm. American Statistician 49: 327–335.
Chib, S., and I. Jeliazkov. 2001. Marginal likelihood from the metropolis-Hastings output. Journal of the American Statistical Association 96: 270–281.
Gelfand, A.E., and A.F.M. Smith. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85: 398–409.
Geman, S., and D. Geman. 1984. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6: 721–741.
Goel, P.K., and M.H. Degroot. 1981. Information about hyperparameters in hierarchical models. Journal of the American Statistical Association 76: 140–147.
Lehmann, E., and G. Casella. 1998. Theory of point estimation. New York: Springer.
Lindley, D.V., and A.F.M. Smith. 1972. Bayes estimates for the linear model. Journal of the Royal Statistical Society B 34: 1–41.
Tanner, M.A., and W.H. Wong. 1987. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82: 528–550.
Tierney, L. 1994. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics 21: 1701–1762.
Wakefield, J.C., A.F.M. Smith, A. Racine-Poon, and A.E. Gelfand. 1994. Bayesian analysis of linear and nonlinear population models using the Gibbs sampler. Applied Statistics 43: 201–221.
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Chib, S., Greenberg, E. (2018). Hierarchical Bayes Models. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2230
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2230
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Online ISBN: 978-1-349-95189-5
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