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Hierarchical Models and More on Convergence Assessment

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Applied Bayesian Statistics

Part of the book series: Springer Texts in Statistics ((STS,volume 98))

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Abstract

So far, all of the Bayesian models that we have encountered have had only two components—the likelihood, which describes the data as draws from a probability distribution, and the prior, which specifies a probability distribution on the unknown parameters in the likelihood. Such a simple model is inadequate for many (probably most) real-world applications. As a result, more complex Bayesian models with additional levels are very commonly used. Such models are called hierarchical models.

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References

  • J. Albert, Bayesian Computation using Minitab (Wadsworth, Belmont, CA, 1997)

    Google Scholar 

  • J. Albert, Bayesian Computation with R (Springer, New York, 2007)

    Book  MATH  Google Scholar 

  • J. Albert, LearnBayes: Functions for Learning Bayesian Inference (2008). R package version 2.0

    Google Scholar 

  • T.W. Anderson, An Introduction to Multivariate Statistical Analysis, 2nd edn. (Wiley, 1984)

    Google Scholar 

  • G. Antelman, Elementary Bayesian Statistics, Edward Elgar Pub (1997)

    Google Scholar 

  • Y. Atchade, J. Rosenthal, Bernoulli 11, 815 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • R.L. Bauer, J. Sung, K.H.E. Jr., A. Koul, N.B. Castillo, T. Nemoto, Annals of Surgical Oncology 4(4), 316 (1997)

    Google Scholar 

  • J.O. Berger, Statistical decision theory and Bayesian analysis (Springer, 1985)

    Google Scholar 

  • D.A. Berry, Statistics: A Bayesian Perspective (Duxbury Press, Belmont, California, 1996)

    Google Scholar 

  • C.I. Bliss, Annals of Applied Biology 22, 134 (1935)

    Article  Google Scholar 

  • G.E. Box, G.C. Tiao, Bayesian inference in statistical analysis (Addison-Wesley, 1973)

    Google Scholar 

  • S.P. Brooks, A. Gelman, Journal of Computational and Graphical Statistics 7, 434 (1998)

    MathSciNet  Google Scholar 

  • R.L. Burden, D. Faires, Numerical Analysis, 9th edn. (Brooks/Cole, Boston, 2011)

    Google Scholar 

  • B.P. Carlin, S. Chib, Journal of the Royal Statistical Society, Series B 57(3), 473 (1995)

    Google Scholar 

  • B.P. Carlin, T.A. Louis, Bayes and Empirical Bayes Methods for Data Analysis, 2nd edn. (Chapman & Hall/CRC, Boca Raton, 2000)

    Book  MATH  Google Scholar 

  • B.P. Carlin, D.J. Sargent, Statistics in Medicine 15, 1093 (1996)

    Article  Google Scholar 

  • S. Chib, Journal of the American Statistical Association 90(432), 1313 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • S. Chib, I. Jeliazkov, Journal of the American Statistical Association 96(453), 270 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • P. Congdon, Bayesian Statistical Modelling (Wiley, 2001)

    Google Scholar 

  • P. Congdon, Applied Bayesian Modelling (Wiley, 2003)

    Google Scholar 

  • M.K. Cowles, Journal of Statistical Planning and Inference 112(1–2) (2003)

    Google Scholar 

  • M.K. Cowles, B.P. Carlin, Journal of the American Statistical Association 91, 883 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • L. Devroye, Non-uniform Random Variate Generation, Springer, (1986)

    Google Scholar 

  • S. DJ, B. NG, C. BP, V. der Linde A, Journal of the Royal Statistical Society, Series B, 64(4), 583 (2002)

    Google Scholar 

  • A.E. Gelfand, A.F.M. Smith, Journal of the American Statistical Association 85, 398 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • A. Gelman, Bayesian Analysis 1(3), 515 (2006)

    MathSciNet  Google Scholar 

  • A. Gelman, D.Rubin, Statistical Science 7, 457 (1992)

    Article  Google Scholar 

  • A. Gelman, X.L. Meng, H. Stern, Statistica Sinica 6, 733 (1996)

    MathSciNet  MATH  Google Scholar 

  • A. Gelman, J.B. Carlin, H.S. Stern, D.B. Rubin, Bayesian Data Analysis, 2nd edn. (Chapman & Hall, 2004)

    Google Scholar 

  • S. Geman, D. Geman, IEEE Transaction on Pattern Analysis and Machine Intelligence 6, 721 (1984)

    Article  MATH  Google Scholar 

  • J. Gill, Bayesian Methods for the Social and Behavioral Sciences (Chapman and Hall, 2002)

    Google Scholar 

  • I.J. Good, The Estimation of Probabilities: An Essay on Modern Bayesian Methods, M.I.T. Press, Cambridge, MA, (1965)

    MATH  Google Scholar 

  • J. Greenhouse, L. Waserman, Statistics in Medicine 14, 1379 (1995)

    Article  Google Scholar 

  • W. Hastings, Biometrika 57, 97 (1970)

    Article  MATH  Google Scholar 

  • D.W. Hosmer, S. Lemeshow, Applied logistic regression (Wiley Series in probability and statistics), 2nd edn. (Wiley-Interscience Publication, 2000)

    Google Scholar 

  • H. Jeffreys, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 186, 453 (1946)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Jensen, Acta Mathematica 30, 175 (1906)

    Article  MathSciNet  MATH  Google Scholar 

  • V. Johnson, J. Albert, Ordinal Data Modeling (Springer, 1999)

    Google Scholar 

  • R.E. Kass, A.E. Raftery, Journal of the American Statistical Association 90(430), 773 (1995)

    Article  MATH  Google Scholar 

  • S.L. Lauritzen, D.J. Spiegelhalter, Journal of the Royal Statistical Society, Series B 50, 205 (1988). Reprinted in Shafer and Pearl (1990)

    Google Scholar 

  • P.M. Lee, Bayesian Statistics: an Introduction, 3rd edn. (Hodder Arnold, 2004)

    Google Scholar 

  • D. Lindley, A. Smith, Journal of the Royal Statistical Society Series B 34, 1 (1972)

    MathSciNet  MATH  Google Scholar 

  • D. Lunn, D. Spiegelhalter, A. Thomas, N. Best, Statistics in Medicine 28, 3049 (2009)

    Article  MathSciNet  Google Scholar 

  • D. Lunn, A. Thomas, N. Best, D. Spiegelhalter, Statistics and Computing 10, 325 (2000)

    Article  Google Scholar 

  • P. McCulloch, J.A. Nelder, Generalized Linear Models, 2nd edn. (CRC Press, 1989)

    Google Scholar 

  • S.B. McGrayne, Scientific American (2011)

    Google Scholar 

  • S.B. McGrayne, The Theory That Would Not Die: How Bayes Rule Cracked the Enigma Code, Hunted Down Russian Submarines and Emerged Triumphant from Two Centuries of Controversy, Yale University Press (2011)

    Google Scholar 

  • N. Metropolis, A. Rosenbluth, A. Rosenbluth, A. Teller, E. Teller, Journal of Chemical Physics 21, 1087 (1953)

    Article  Google Scholar 

  • D.S. Moore, The Basic Practice of Statistics, 4th edn. (W.H. Freeman and Company, New York, 2007)

    Google Scholar 

  • R.M. Neal, Annals of Statistics 31, 705 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • J.A. Nelder, R.W.M. Wedderburn, Journal of the Royal Statistical Society, Series A, General 135, 370 (1972)

    Google Scholar 

  • M. Novick, P. Jackson, D. Thayer, N. Cole, British Journal of Mathematical and Statistical Psychology 25, 33 (1972)

    Article  MATH  Google Scholar 

  • S.P. Poplack, A.N. Tosteson, M.R. Grove, W.A. Wells, P.A. Carney, Radiology 217, 832 (2000)

    Google Scholar 

  • R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2008). URL http://www.R-project.org. ISBN 3-900051-07-0

  • C.P. Robert, G. Casella, Introducing Monte Carlo Methods with R (Springer, 2010)

    Google Scholar 

  • D.J. Spiegelhalter, L.S. Freedman, M. Parmer, Statistics in Medicine 11, 1501 (1993)

    Article  Google Scholar 

  • D. Spiegelhalter, A. Thomas, N. Best, W. Gilks, BUGS Examples, Version 0.5. MRC Biostatistics Unit, Cambridge (1995)

    Google Scholar 

  • C.P. Robert, The Bayesian choice, Springer (2007)

    Google Scholar 

  • G.G. Woodworth, Biostatistics: A Bayesian Introduction (Wiley, Hoboken, New Jersey, 2004)

    MATH  Google Scholar 

  • A. Zellner, An Introduction to Bayesian Inference in Econometrics (Wiley, 1971)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa, USA

    Mary Kathryn Cowles

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  1. Mary Kathryn Cowles
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Cowles, M.K. (2013). Hierarchical Models and More on Convergence Assessment. In: Applied Bayesian Statistics. Springer Texts in Statistics, vol 98. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5696-4_9

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