Convergence of Dirichlet Measures and the Interpretation of Their Parameter.
Abstract
The form of the Bayes estimate of the population mean with respect to a Dirichlet prior with parameter alpha has given rise to the interpretation that alpha(Chi) is the prior sample size. Furthermore, if alpha(Chi) is made to tend to zero, then the Bayes estimate mathematically converges to the classical estimator, namely the sample mean. This has further given rise to the general feeling that allowing alpha(Chi) to become small not only makes the 'prior samples size' small but also that it corresponds to no prior information. By investigating the limits of prior distributions as the parameter alpha tends to various values, we show that it is misleading to think of alpha(Chi) as the prior sample size and the smallness of alpha(Chi) as no prior information. In fact very small values of alpha(Chi) actually mean that we have very definite information concerning the unknown true distribution. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1981
- Accession Number
- ADA101688
Entities
People
- Jayaram Sethuraman
- Ram C. Tiwari
Organizations
- Florida State University