Abstract
Two large classes of parametric inference are frequentist and Bayesian methods. Frequentist methods assume that \(\boldsymbol{\theta }\) are constant parameters “generated by nature,” while Bayesian methods assume that the parameters \(\boldsymbol{\theta }\) are random variables. Chapters 1–10 consider frequentist methods with an emphasis on exponential families, but Bayesian methods also tie in nicely with exponential family theory.
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References
Berger, J.O., Boukai, B., and Wang, Y. (1997), “Unified Frequentist and Bayesian Testing of a Precise Hypothesis,” Statistical Science, 12, 133–160.
Berry, D.A., and Lindgren, B.W. (1995), Statistics, Theory and Methods, 2nd ed., Duxbury Press, Belmont, CA.
Bolstad, W.M. (2004, 2007), Introduction to Bayesian Statistics, 1st and 2nd ed., Wiley, Hoboken, NJ.
Carlin, B.P., and Louis, T.A. (2009), Bayesian Methods for Data Analysis, 3rd ed., Chapman & Hall/CRC Press, Boca Raton, FL.
Casella, G., and George, E.I. (1992), “Explaining the Gibbs Sampler,” The American Statistician, 46, 167–174.
DeGroot, M.H., and Schervish, M.J. (2012), Probability and Statistics, 4th ed., Pearson Education, Boston, MA.
Frey, J. (2013), “Data-Driven Nonparametric Prediction Intervals,” Journal of Statistical Planning and Inference, 143, 1039–1048.
Grübel, R. (1988), “The Length of the Shorth,” The Annals of Statistics, 16, 619–628.
Hyndman, R.J. (1996), “Computing and Graphing Highest Density Regions,” The American Statistician, 50, 120–126.
Lavine, M., and Schervish, M.J. (1999), “Bayes Factors: What They Are and What They Are Not,” The American Statistician, 53, 119–122.
Lindley, D.V. (1972), Bayesian Statistics: a Review, SIAM, Philadelphia, PA.
Morris, C.N. (1983), “Natural Exponential Families with Quadratic Variance Functions: Statistical Theory,” The Annals of Statistics, 11, 515–529.
Robert, C.P., and Casella, G. (2010), Monte Carlo Statistical Methods, Springer, New York, NY.
Smith, A.F.M, and Gelfand, A.E. (1992), “Bayesian Statistics Without Tears: a Sampling-Resampling Perspective,” The American Statistician, 46, 84–88.
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Olive, D.J. (2014). Bayesian Methods. In: Statistical Theory and Inference. Springer, Cham. https://doi.org/10.1007/978-3-319-04972-4_11
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DOI: https://doi.org/10.1007/978-3-319-04972-4_11
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