To learn more about EpiX Analytics' work, please visit our modeling applications, white papers, and training schedule.

Page tree


The idea

The results for the Binomial and Negative Binomial distributions are both modeling randomness: that is to say that they are returning probability distributions of possible future outcomes. At times, however, we are looking back at the results of a binomial process and wish to determine one of the parameters. For example, we may have observed n trials of which s were successes and from that information would like to estimate p. This binomial probability is a fundamental property of the stochastic system and can never be observed, but we can become progressively more certain about its true value by collecting data.

modeling the uncertainty about p

Bayesian statistics

If we have observed s successes in n random trials, a Bayesian analysis gives the conveniently simple result:

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

where a Beta(a,b,1) prior is assumed.

The Beta(1,1,1) is a Uniform(0,1) distribution - often considered appropriate as an uninformed prior, in which case we have:

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

The Beta distribution can be used this way because it is a conjugate distribution to the binomial likelihood function.

Classical statistics

Three methods for the estimation of p are discussed here.

Comparison between estimation methods

A comparison of the classical and Bayesian methods of estimating p is provided here.

  • No labels