Prior Distribution Classes with Comprehensive Coverage

Yıl 2010, Cilt: 7 Sayı: 1, 18 - 40, 15.07.2010

Oya Ekici

https://izlik.org/JA48CB89RY

Öz

The Bayes’ theorem which is the kernel of today’s Bayesian World incorporates prior knowledge in analysis. Regarding its level, form or application restrictions, the challenging part can be seen as “prior” especially for joiners in this world. In various areas, concerning the requirements, there are various prior distributions suggested to be used. However the studies that give a generic look and review on prior distributions classes are not seen in the literature. With this motivation, the paper discusses prior distributions with comprehensive coverage. Thus it’s aimed to introduce prior distribution classes and to give a review on them.

Anahtar Kelimeler

Classes of prior distributions , Informative priors , Non-informative priors

Kapsamlı Bir İçerikle Ön Dağılım Türleri

https://izlik.org/JA48CB89RY

Öz

Bayesyen analizlerin özünü oluşturan Bayes Teoremi, analizlere ön bilgiyi dahil ederek istatistiksel süreci gerçekleştirmektedir. Ön bilginin düzeyi, yapısı ve uygulama sınırları gözönüne alınınca, özellikle bu alanda yeni çalışan araştırmacılar için en zorlayıcı kısmı “ön dağılım” olarak görülebilir. Farklı alanlarda ihtiyaç doğrultusunda önerilen çeşitli ön dağılım türleri vardır. Öte yandan ön dağılımlar üzerine jenerik bir bakışı yansıtan ve gözden geçirme niteliğinde çalışma literatürde mevcut değildir. Bu motivasyonla, çalışma ön dağılım türlerini kapsamlı bir içerikle ele almaktadır. Böylelikle araştırmacılara ön dağılım türlerinin tanıtımı ve bunlarla ilgili genel bir bakış kazandırmak amaçlanmaktadır.

Anahtar Kelimeler

Ön dağılım türleri , Bilgi veren ön dağılımlar , Bilgi vermeyen ön dağılımlar

Kaynakça

• Berger, J. O., 1985. Statistical decision theory and Bayesian analysis. 2.ed., New York, Springer-Verlag Inc., 617.
• Berger, J., 2006. The case for objective Bayesian analysis. Bayesian Analysis, 1(3):385-402.
• Berger, J. O., Bernardo, J.M., 1992. On the development of reference priors. Bayesian Statistics 4 (J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith, eds) Oxford: University Press, 35-60 (with discussions).
• Berger, J.O., Pericchi, L. R., 1996. The intrinsic Bayes factor for model selection and prediction.”J. Amer. Statist. Assoc., 91:109-122.
• Bernardo, J. M., 1979. Reference posterior distributions for Bayesian inference. Journal of the Royal Statististical Society, B(41): 113-147.
• Bernardo, J. M., 1996. Noninformative priors do not exist: A discussion with Jose M. Bernardo. Journal of Statistical Planning and Inference, 5 December 1996.
• Box, G.E. P, Tiao, G. C., 1992. Bayesian inference in statistical analysis. Wiley Clkassics Library Edition, New York, John Wiley & Sons, 588.
• Cano, J. A., Kessler, M., Salmeron, D., 2007. Integral priors for the one way random effects model. Bayesian Analysis, 2(1):59-68.
• Cano, J. A., Kessler, M., Moreno, E., 2004. On intrinsic priors for nonnested models. Test, 13(2): 445-463.
• Cano, J. A., Salmeron, D., Robert, C. P., 2007. Integral equation solutions as prior distributions for Bayesian model selection. Test, Published online March 2007, DOI name 10.1007/s11749-006-0040-8.
• Demirhan, H., Hamurkaroğlu, C., 2008. Bayesian estimation of log odds ratios from R×C and 2×2×K contingency tables. Statistica Neerlandica, 62(4): 405–424.
• Diaconis, P., Ylvisaker, D., 1985. Quantifying prior opinion, in Bayesian statistics 2, J.M. Bernardo, M.H. DeGroot, D.V. Lindley and A.F.M. Smith (eds.), Amsterdam: North Holland Press.
• Ekici, O., Yorulmaz, Ö., 2008. The relationship of aberrant observation and structural break point: Determination with Bayesian autoregressive process. Doğuş University Journal, 9(2):146-157.
• Galavotti, M. C., 2001. Subjectivism, Objectivism and Objectivity in Bruno de Finetti’s Bayesianism. Foundations of Bayesianism, Ed. David Corfield and Jon Williamson, Kluwer Academic Publishers, 413.
• Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B., 1995. Bayesian data analysis, London, Chapman & Hall, 526.
• Gelman, A., 2002. Prior distribution. Encyclopedia of Environmetrics, John Wiley & Sons Ltd., Chichester, 3: 1634–1637
• Gelman, A., 2009. Prior distributions for Bayesian data analysis in political science. Frontier of Statistical Decision Making and Bayesian Analysis, in honor of James O. Berger.
• Gill, J., 2002. Bayesian methods, New York, Chapman & Hall, 2002, 459.
• Hartigan, J., 1964. Invariant prior distributions. The Annals of Mathematical Statistics, 35: 836-845.
• Ibrahim J. G., Chen, M. H., 2000. Power prior distributions for regression models. Statistical Science, 15(1): 46-60.
• Ibrahim J. G., Chen M.-H., Sinha D., 2003. On optimality properties of the power prior. Journal of the American Statistical Association, 98: 204-213.
• Jaynes, E. T., 1968. Prior probabilities. IEEE Transactions on Systems Science and Cybernetics, SSC-4, 227-241, (Reprinted in Roger D. Rosenkrantz, Compiler. (1983 . E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics. Dordrecht, Holland: Reidel Publishing Company, 116-130).
• Kass, R. E., Wasserman, L., 1996. The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91(435): 1343-1362.
• Lindley, D.V., 1965. Introduction to probability and statistics from a Bayesian viewpoint, Part 2, London, Cambridge University Press, 292.
• Litterman, R.B., 1986. Forecasting with Bayesian vector autoregressions-five years of experience. Journal of Business & Economic Statistics, 4: 25-38
• Maddala, G.S., Kim, M., 2002. Unit roots, cointegration and structural change. Cambridge University Press, 505.
• Philips, P.C., 1991. To criticize the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics, 6(4):333-364.
• Popper, K.R., 2003. Bilimsel araştırmanın mantığı, Çev. İlknur Aka, İbrahim Turan, 2.B, İstanbul, Yapı Kredi Yayınları, Kazım Taşkent Klasik Yapıtlar Dizisi, 2003, 596.
• Raiffa, H., Schlaifer, R., 1968. Applied statistical decision theory. America, MIT Press, 356.
• Sims, C.A., 1988. Bayesian skepticism on unit root econometrics. Journal of Economic Dynamics and Control, 12: 463-474.
• Sivia, D.S., 1996. Data analysis, a Bayesian tutorial. New York, Oxford Unv. Press, 189.
• Wasserman, L., 2006. Frequentist Bayes is objective (Comment on Articles by Berger and Goldstein). Bayesian Analysis, 1(3): 451-456.
• Yardımcı, A., 1992. Çoklu bağlantılı çoklu doğrusal regresyonda Bayes yaklaşımı. Y.L., Fen Bilimleri Enstitüsü, Hacettepe Ünv., 72
• Zellner, A., 1971. An introduction to Bayesian inference in econometrics. New York, John Wiley & Sons, 431.
• Zellner, A., 1986. On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In Goel, P. And Zellner, A. (eds.), Bayesian Inference and Decision Techniques, 233-243. Amsterdam: Elsevier Science Publishers B.V.