Uncertainty about a probability, fraction or prevalence | Vose Software

Uncertainty about a probability, fraction or prevalence

In risk analysis, we are frequently faced with having to estimate a probability, a fraction or a prevalence. We usually have some data that would help us produce this estimate, that come from surveys, experiments, or even computer simulations. If we can be sure that the data are collected according to a binomial process, we can use the Beta distribution to describe our uncertainty about the prevalence, fraction or probability by applying the formula:

p = Beta(s+1, n-s+1)

where n is the number of trials or samples, and s is the number of 'successes'.

The Beta distribution has a domain of [0,1] so is an immediate contender to model uncertainty or randomness about a probability, fraction or prevalence. However, there are more technical reasons for using the Beta distribution here; namely that it is the conjugate to the Binomial distribution and the above formula is the result of a Bayesian inference calculation with an uninformed prior. Translation for the layperson: the Beta distribution is the direct result of a statistical analysis where we assume that the data come from a binomial process, and where we knew nothing about the parameter p being estimated, prior to collecting these data.