Convergence of Dirichlet Measures and the Interpretation of Their Parameter.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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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 alphaChi is the prior sample size. Furthermore, if alphaChi 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 alphaChi 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 alphaChi as the prior sample size and the smallness of alphaChi as no prior information. In fact very small values of alphaChi actually mean that we have very definite information concerning the unknown true distribution. Author
- Statistics and Probability