Department of Mathematics Colloquium

University of Idaho

Spring 2012

Thursday,  April 12, 3:30-4:20 pm, room TLC 032

Refreshments in Brink 305 at 3:00 pm

Using Maximum Entropy and Bayesian Analysis to Develop
Non-parametric Probability Distributions for the Mean and Variance


Bahman Shafii

Statistical Programs

University of Idaho


Estimation of moments such as the mean and variance of populations is generally carried out through sample estimates. Given normality of the parent population, the distribution of sample mean and sample variance is straightforward. However, when normality cannot be assumed, inference is usually based on approximations through the use of the Central Limit theorem. Furthermore, the data generated from many real populations may be naturally bounded; i.e., weights, heights, etc. Thus, a normal population, with its infinite bounds, may not be appropriate, and the distribution of sample mean and variance is not obvious. Using Bayesian analysis and maximum entropy, procedures are developed which produce distributions for the sample mean, as well as combined mean and variance. These methods require no assumptions on the form of the parent distribution or the size of the sample and inherently make use of existing bounds.