Fisher Information, stochastic processes and generating functions

Abstract: 

In this talk, we deliver our theoretical and numerical results on the Fisher Information for the birth rate of a partially-observable simple birth process involving n observations. Our goal is to estimate the rate of growth, lambda, of a population governed by a simple birth process. We may choose n time points at which to count the number of individuals present, but due to detection difficulties, or constraints on resources, we are able only to observe each individual independently with fixed probability p. We discuss the optimal times at which to make our n observations in order to maximise the Fisher Information for the birth rate lambda. Finding an analytical form of the Fisher Information in general appears intractable. Nonetheless, we find a very good approximation for the Fisher Information by exploiting the probabilistic properties of the underlying stochastic process. Both numerical and theoretical results strongly support the latter approximation and confirm its high level of accuracy. However, this approximation is limited to the number of observations. Eventually, we utilised the concept of generating functions to calculate the Fisher Information efficiently.

The seminar will be followed by drinks and finger food. All attendees are welcome!