Mathematical Sciences: Nonparametric Function Estimation andStochastic Modeling

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This reseach will focus on several problems in applied probability and statistics which stem from biophysical experiments that aim to measure current flow through ionic channels in cell membranes. This measurements are usually noisy binary signals; the mathematical model usually used by neurophysiologists is that the state of the molecule is a Markov jump process with a finite state space, and that the observed data is a function of that process. The fundamental reseach questions are: What may be learned about the Markov process from the observations, and how may it be learned? Other research topics in the area of nonparametric function estimation and smoothing will also be studied. This research is in the general area of statistical time series analysis. This research will focus on developing better methods to get information from data that can take on only one of two values at any given time, but that can move from one state to the other as time goes by. Such data is a common result of biophysical experiments and this research promises to inhance and, to make more efficient, the accrual of knowledge from biophysical research.