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Maximum entropy and goodness-of-fit tests
Supervisor: Oliver Johnson
Theme: Applied Probability
Recent work has used the fact that certain random variables satisfy a maximum entropy property, to perform a goodness-of-fit test. For example, the Gaussian distribution maximizes entropy under a variance constraint. Then, given data from some distribution, a statistician can decide whether this distribution was indeed normal, by estimating its entropy and seeing if it matches the value obtained by the Gaussian. The main aims of this project would be
(a) to consider new ways of estimating the entropy
(b) to extend the class of random variables that we can test for, to include random variables such as the Poisson distribution.