Showing papers on "Latent Dirichlet allocation published in 1979"

Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes

Abstract: The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters gets larger than 2 or 3 we propose two approximations for estimators of a particular parameter and compare their performance using examples.

Credibility and the Dirichlet process

Abstract: Credibilists usually side-step the problem of specifying the structure function for a collective of risk experiences by finding certain projections in certain Hilbert spaces. These projections represent approximations to the Bayes rule. However, since both the credibility mean and credibility distribution function are proper Bayes relative to a Dirichlet process prior it is natural for the present paper to investigate the suitability of this process as a structure function. The proposed nonparametric models provide some increased insight into the credibility factor Z and the manual premium m; in particular, novel estimators for them are suggested.