Physics Colloquium - Spring 2007 - Parameters of stochastic diffusion processes estimated from observations of first hitting-times: application to the leaky integrate-and-fire neuronal model
Dept of Physics & Astronomy
University of Maine, Orono, Maine
Presents
Susanne Ditlevsen
Associate Professor
Dept. of Biostatistics, University of Copenhagen
Parameters of stochastic diffusion processes estimated from observations of first hitting-times: application to the leaky integrate-and-fire neuronal model
The first hitting-time to a constant threshold of a diffusion process has been in focus for stochastic modeling of problems where a hidden random process only shows when it reaches a certain level that triggers some observable event. Applications come from various fields, e.g. neuronal modeling, survival analysis, mathematical finance, and more generally from physics, biology, finance, engineering and many others.
Apart from studying properties of the models themselves, methods for model verification are equally important. The first step is to identify model parameters estimated from experimental data, then statistical comparison between the model and the data can be performed. In many applications where renewal point data are available, models of first hitting-times of underlying diffusion processes arise. Despite of the seemingly simplicity of the model, the problem of how to estimate parameters of the underlying stochastic process has resisted its solution. The few attempts have either been unreliable, difficult to implement or only valid in subsets of the relevant parameter space. In this talk a newly developed estimation method that overcomes these difficulties is presented, it is computationally easy and fast to implement, and also works surprisingly well on small data sets. It is a direct application of the Fortet integral equation. The method is illustrated on simulated data and applied to recordings of neuronal activity. It also provides a diagnostic tool, which in the neuronal setting can distinguish between bursting and non-bursting behavior.
Friday, February 16, 2007
3:10 pm
140 Bennett Hall
Refreshments will follow in Rm. 114, Bennett Hall
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