Mathematical Sciences: Statistical Inference for Some Dynamic Phenomena

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The principal investigator will develop stochastic models and statistical methods for handling data recorded on phenomena evolving in time and/or distributed in space. Because of the complexity of the data, the subject matter of the substantive field will play a crucial role in modelling and analysis; however it is anticipated that the techniques developed will be broadly applicable. Variants of techniques for ordinary random variables will be developed for complex random functions. Some of the particular problems to be studied are: 1) parameter estimation and input signal design for the bilinear system basic to nuclear magnetic resonance spectroscopy, 2) technique development for modelling and discerning the structure of collections of interacting point processes as applicable to networks of firing nerve cells. The investigator will obtain both theoretical and applied results for the problems studied. The principal investigator will develop stochastic model and statistical methods for handling data recorded on phenomena evolving in time and/or distributed in space. Because of the complexity of the data, the subject matter of the substantive field will play a crucial role in modelling and analysis; however it is anticipated that the techniques developed will be broadly applicable. Variants of techniques for ordinary random variables will be developed for complex random functions. Some of the particular problems to be studied are: 1) parameter estimation and input signal design for the bilinear system basic to nuclear magnetic resonance spectroscopy, 2) technique development for modelling and discerning the structure of collections of interacting point processes as applicable to networks of firing nerve cells. The investigator will obtain both theoretical and applied results for the problems studied.