Abstract
Let θ = (θ1,...,θk) be the parameters for k independent binomial random variables. We wish to estimate θ under the restriction θ ∊ R where R is a k-dimensional subset of the full parameter space {θ; 0 ≤ θi ≤ 1, i = 1,...,k}. Bayes estimators (means of posteriors) are developed for θ which correspond to prior distributions that assign probability one to the set R. Since the support of the resulting posterior is R, the posterior mean will be in R if R is a convex set. A bioassay example is given where the parameters are assumed to be increasing, or increasing and S-shaped.
This research was partially supported by an NSERC grant from the Canadian government while the author was a visiting professor in the Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario.
Chapter PDF
Similar content being viewed by others
References
Barlow, R.E., Bartholomew, D.J., Bremner, J.M., and Brunk, H.D., 1972, Statistical Inference Under Order Res trictions, Wiley, New York.
Broffitt, J.D., 1984, “A Bayes estimator for ordered parameters and isotonic Bayesian graduation,” Scand. Actuarial J., 231–247.
Broffitt, J.D., 1986, “Isotonic Bayesian graduation with an additive prior,” Actuarial Science-Festschrift in Honour of Professor V.M. Joshi’s 70th Birthday, vol.6, I.B. MacNeill and G.J. Umphrey, eds., 19–40.
Schmoyer, R.L. 1984, “Sigmoidally constrained maximum likelihood estimation in quantal bioassay,” J. Amer. Statist. Assoc. 79:448–453.
Sedransk, J., Monahan, J. and Chiu, H.Y., 1986, “Bayesian estimation of finite population parameters in categorical data models incorporating order restrictions,” J. Royal Statist. Soc. Ser. B. 47:519–527.
Smith, A.M.F., 1977, “A Bayesian note on reliability growth during a development testing program,” IEEE Trans. Reliability, R-26:346–347.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Broffitt, J.D. (1987). Restricted Bayes Estimates for Binomial Parameters. In: Viertl, R. (eds) Probability and Bayesian Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1885-9_7
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1885-9_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9050-6
Online ISBN: 978-1-4613-1885-9
eBook Packages: Springer Book Archive