Applications of the Beta Distribution Part 1: Transformation Group Approach

A transformation group approach to the prior for the parameters of the beta distribution is suggested which accounts for finite sets of data by imposing a limit to the range of parameter values under consideration. The relationship between the beta distribution and the Poisson and gamma distributions in the continuum is explored, with an emphasis on the decomposition of the model into separate estimates for size and shape. Use of the beta distribution in classification and prediction problems is discussed, and the effect of the prior on the analysis of some well known examples from statistical genetics is examined.