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

Page tree

Versions Compared


  • This line was added.
  • This line was removed.
  • Formatting was changed.
Comment: Updated links



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


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.