A Bayesian Approach for Parameter Estimation in Logistic Regression

Yıl 2012, Cilt: 12 Sayı: 1, 15 - 22, 01.04.2012

Mehmet Ali Cengiz Erol Terzi Talat Şenel Naci Murat

Öz

Anahtar Kelimeler

-

Lojistik Regresyonda Parametre Tahmininde Bayesci Bir Yaklaşım

Öz

İstatistikte Bayesci çıkarım, ilave bir bilgi öğrenildiğinde bir parametrenin sonsal tahminini güncellemede Bayes kuralını kullanan bir çıkarım metodudur. Bayesci güncelleme İstatistikte özellikle matematiksel istatistikte önemli bir yöntemdir. Bir istatistiksel metot için Bayesci çıkarım otomatik olarak herhangi bir hesaplama metodu kadar iyi çalışır. Bu çalışmada iki gerçek veri üzerinde Lojistik regresyon için Bayesci yaklaşım verilmiştir.

Anahtar Kelimeler

Bayesci Yaklaşım, Lojistik Regresyon, MCMC

Kaynakça

• Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis, New York: Springer- Verlag.
• Berger, J.O., 2006. The Case for Objective Bayesian Analysis. Bayesian Analysis, 3,385–402.
• Berger, J.O. and Wolpert, R., 1988. The Likelihood Principle, 9, Second Edition, Hayward, California: Institute of Mathematical Statistics, monograph series.
• Bernardo, J.M. and Smith, A.F.M., 1994. Bayesian Theory, New York: John Wiley & Sons.
• Bernardo, J.M. and Smith, A.F.M., 2000. Bayesian Theory, New York: John Wiley & Sons.
• Carlin, B.P. and Louis, T.A., 2000. Bayes and Empirical Bayes Methods for Data Analysis, Second Edition, London: Chapman & Hall.
• Chen, M.H., Shao, Q.M. and Ibrahim, J.G., 2000. Monte Carlo Methods in Bayesian Computation, New York: Springer-Verlag.
• Congdon, P., 2001. Bayesian Statistical Modeling, John Wiley & Sons.
• Congdon, P., 2003. Applied Bayesian Modeling, John Wiley & Sons.
• Congdon, P., 2005. Bayesian Models for Categorical Data, John Wiley & Sons.
• Gelfand, A.E., Hills, S.E., Racine-Poon, A. and Smith, A.F.M., 1990. llustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling. Journal of the American Statistical Association, 85, 972– 985.
• Gelman, A., Carlin, J., Stern, H. and Rubin, D., 2004. Bayesian Data Analysis, Second Edition, London: Chapman & Hall.
• Geman, S. and Geman, D., 1984. Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images. IEEE Transaction on Pattern Analysis and Machine Intelligence, 6, 721–741.
• Gilks, W.R., Richardson, S. and Spiegelhalter, D.J., 1996. Markov Chain Monte Carlo in Practice, London: Chapman & Hall.
• Goldstein, M., 2006. Subjective Bayesian Analysis: Principles and Practice. Bayesian Analysis, 3, 403– 420.
• Jeffreys, H., 1961. Theory of Probability, third Edition, Oxford: Oxford University Press.
• Kass, R.E. and Wasserman, L., 1996. Formal Rules of Selecting Prior Distributions: A Review and Annotated Bibliography. Journal of the American Statistical Association, 91, 343–370.
• Liu, J.S., 2001. Monte Carlo Strategies in Scientific Computing, Springer-Verlag.
• O’Hagan, A., 1994. Bayesian Inference, volume 2B of Kendall’s Advanced Theory of Statistics, London: Arnold.
• Robert, C.P., 2001. The Bayesian Choice, Second Edition, New York: Springer-Verlag.
• Robert, C.P. and Casella, G., 2004. Monte Carlo Statistical Methods, 2nd ed. New York: Springer- Verlag.
• Tanner, M.A., 1993. Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, New York: Springer-Verlag.
• Wasserman, L., 2004. All of Statistics: A Concise Course in Statistical Inference, New York: Springer- Verlag.