Inference from noninformative ML-II priors

• Autorzy: Kopciuszewski P.
• Języki publikacji: EN

Abstrakty

EN

The type II maximum likelihood (ML-II) is considered in this paper. The problem of finding the ML-II prior is too complex, in many cases. But we propose some methods of approximation ML-II prior. Both noninformative and informative ML-II priors are considered. If no information is given about unknown prior then we will construct a proper density which is approximately ML-II prior. The theorem which let us approximate ML-II prior belonging to the given class of densities is formulated. The methods of approximation ML-II prior are simply and easy to applied. All required calculations are done by MCMC algorithms.

Słowa kluczowe

EN

type II maximum likelihood; approximation methods

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2004
• Tom: Vol. 3, nr 1
• Strony: 61--66
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Kopciuszewski P.

• Institute of Mathematics and Computer Science, Czestochowa University of Technology

Bibliografia

• [1] Berger J., Berliner L., Robust Bayes and empirical Bayes analysis with ε-contaminated priors, Ann. Statist., (1986), 14, 461-486.
• [2] Chaturvedi A., Robust Bayesian analysis of the linear regression model. J. Statist. Plann. Infer., (1993), 50, 175-186.
• [3] Evans M., Swartz T., Methods for approximating integrals in statistics with special emphasis on bayesian integration problems, Statist. Sci., (1995), 10, 254-272.
• [4] Good I.J., The estimation of probabilities, M.I.T. Press, Cambridge (1965).
• [5] Good I.J., Good Thinking: The Foundations of Probability and Its Applications, University of Minesota Press, Minneapolis, (1983).
• [6] Gosh M., Kim D.H., Robust Bayes competitors of the ratio estimator. Statist. Decisions, (1997), 15, 17-36.
• [7] Lee C.B., Bayesian analysis of a change-point in exponential families with applications. Comp. Statist. Data Anal., (1998), 27, 195-208.
• [8] Moreno E., Carmona A.G., Empirical Bayes analysis for ε-contaminated priors with shape and quantile constraints. Rebrape, (1990), 4, 177-200.
• [9] Robert C.P., The Bayesian choice. Springer-Verlag, New York, (1997).
• [10] Sivaganesan S., Sensitivity of some standard Bayesian estimates to prior uncertainty: A comparison. J. Statist. Plann. Infer., (1991), 27, 85-103.
• [11] Sivaganesan S., Berger J., Ranges of posterior measures for priors with unimodal contaminations, Ann. Statist., (1989), 17, 868-889.
• [12] Ross M.S., Statistical modelling and decision science. Academic Press, Berkeley (1997).
• [13] Tierney L., Markov chain for exploring posterior distributions Ann. Statist., (1994) 22, 1701-1762.
• [14] Waal D.J., Nel D.G., A procedure to select a ML-II prior in a multivariate normal case, Comm. Statist. Simulation Comput., (1988), 17, 1021-1035.