Mathematical Sciences: Nonparametric Function Estimation andStochastic Modeling

本研究将集中在应用概率和统计的几个问题，这些问题源于生物物理实验，旨在测量通过细胞膜离子通道的电流。这种测量通常是有噪声的二进制信号；神经生理学家通常使用的数学模型是，分子的状态是一个具有有限状态空间的马尔可夫跳跃过程，而观察到的数据是该过程的函数。基本的研究问题是：从观察中可以了解到关于马尔可夫过程的什么，以及如何了解它？在非参数函数估计和平滑领域的其他研究课题也将被研究。本研究属于统计时间序列分析的一般范畴。这项研究将侧重于开发更好的方法，从数据中获取信息，这些数据在任何给定时间只能呈现两种值中的一种，但随着时间的推移，可以从一种状态转移到另一种状态。这些数据是生物物理实验的常见结果，这项研究有望提高生物物理研究知识的积累，并提高效率。

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.