 STATISTICS SEMINAR
 Speaker: Dr Ali Eshragh, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Fisher information, stochastic processes and generating functions
 Location: Room V105, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Fri, 18^{th} Mar 2016
 Abstract:
In this talk, we deliver our theoretical and numerical results on the Fisher Information for the birth rate of a partiallyobservable 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 more efficiently.
 Download: Talk slides (776KB)
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 CARMA COLLOQUIUM
 Speaker: Dr Ali Eshragh, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Binomial Observations, Fisher Information and Optimal Sampling Times
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 14^{th} Nov 2013
 Abstract:
Our goal is to estimate the rate of growth of a population governed by a simple stochastic model. We may choose (n) sampling times 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 with fixed probability (p). We discuss the optimal sampling times at which to make our observations in order to approximately maximize the accuracy of our estimation. To achieve this, we maximize the expected volume of information obtained from such binomial observations, that is the Fisher Information. For a single sample, we derive an explicit form of the Fisher Information. However, finding the Fisher Information for higher values of (n) appears intractable. Nonetheless, we find a very good approximation function for the Fisher Information by exploiting the probabilistic properties of the underlying stochastic process and developing a new class of delayed distributions. Both numerical and theoretical results strongly support this approximation and confirm its high level of accuracy.
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