Abstract
Until the advent of powerful and accessible computing methods, the experimenter was often confronted with a difficult choice. Either describe an accurate model of a phenomenon, which would usually preclude the computation of explicit answers, or choose a standard model which would allow this computation, but may not be a close representation of a realistic model. This dilemma is present in many branches of statistical applications, for example, in electrical engineering, aeronautics, biology, networks, and astronomy. To use realistic models, the researchers in these disciplines have often developed original approaches for model fitting that are customized for their own problems. (This is particularly true of physicists, the originators of Markov chain Monte Carlo methods.) Traditional methods of analysis, such as the usual numerical analysis techniques, are not well adapted for such settings.
There must be, he thought, some key, some crack in this mystery he could use to achieve an answer.
—P.C. Doherty, Crown in Darkness
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Diebolt, J. and Robert, C. (1994). Estimation of finite mixture distributions by Bayesian sampling. J. Royal Statist. Soc. Series B, 56: 363–375.
Jeffreys, H. (1961). Theory of Probability (3rd edition). Oxford University Press, Oxford.
Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York, second edition.
Casella, G. (1996). Statistical theory and Monte Carlo algorithms (with discussion). TEST, 5: 249–344.
Bernardo, J. and Smith, A. (1994). Bayesian Theory. John Wiley, New York.
Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (with discussion). In Bernardo, J., Berger, J., Dawid, A., and Smith, A., editors, Bayesian Statistics 4, pages 169–193. Oxford University Press, Oxford.
Bernardo, J. (1979). Reference posterior distributions for Bayesian inference (with discussion). J. Royal Statist. Soc. Series B, 41: 113–147.
Wakefield, J., Smith, A., Racine-Poon, A., and Gelfand, A. (1994). Bayesian analysis of linear and non-linear population models using the Gibbs sampler. Applied Statistics (Ser. C), 43: 201–222.
Seidenfeld, T. and Wasserman, L. (1993). Dilation for sets of probabilities. Ann. Statist., 21: 1139–1154.
Efron, B. (1979). Bootstrap methods: another look at the jacknife. Ann. Statist., 7: 1–26.
Efron, B. (1982). The Jacknife, the Bootstrap and Other Resampling Plans, volume 38. SIAM, Philadelphia.
Diaconis, P. and Holmes, S. (1994). Gray codes for randomization procedures. Statistics and Computing, 4: 287–302.
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Robert, C.P., Casella, G. (2004). Introduction. In: Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4145-2_1
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DOI: https://doi.org/10.1007/978-1-4757-4145-2_1
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