Calculate the alpha and beta parameters for Beta probability distributions, based on either specified values for the mode and 5th or 95th percentile of the distribution, or on count data, or summarise Beta probability distributions for given alpha or beta parameters. See the User Guide or Suess et al. (2002) for more details on parameter estimation based on mode and percentiles.
Beta distributions are a type of probability distribution that is commonly used to describe uncertainty about the true value of a proportion, such as sensitivity, specificity or prevalence. They are appropriate distributions to express uncertainty about the prior values for prevalence, sensitivity or specificity in the Gibbs sampler (Joseph et al., 1995; Vose, 2000). When used for this purpose, the Beta distribution can be defined by the two parameters, alpha and beta (written as Beta(alpha, beta)), with alpha = x + 1 and beta = n - x + 1, where x is the number of positive events out of n trials. As n increases, the degree of uncertainty (the width of the distribution) about the estimated proportion (x/n) decreases. Alternatively alpha and beta parameters can be estimated from the mode and a given percentile, if suitable data is not available.
If there is no prior information on which to base a prior distribution, alpha = beta = 1 should be used. This results in a uniform (uninformed) distribution, in which all values between 0 and 1 have equal probability of occurrence.
Parameters can be estimated for as many distributions as you wish, simply by providing the appropriate data. To estimate parameters:
The program expects two columns of data, either mode and percentile, counts, or alpha and beta parameters. Distribution parameters will be calculated and distribution summaries presented for each pair of values provided:
Outputs from this program are the alpha and beta parameters for each distribution, which can then be used as inputs for other analyses. Numeric summaries and density plots for each distribution are also provided.