A seminar by Professor Edward L Boone from Virginia Commonwealth University
Title: Statistical Inference on Fractional Partial Differential Equations
Abstract: Researchers are often confronted with connecting theoretical models with real world data. This is very common in the petroleum resources industry. Specifically, they wish to understand the pressure of gas in a porous substance. A wealth of mathematical models have been developed based on partial differential equations and have been studied extensively. These modeling efforts have been extended to using Fractional Partial Differential Equations (FPDE) to better capture various attributes of the process. The problem for researchers arises when one needs to estimate the fractional parameter. As the fractional parameter is not a parameter in the traditional statistical sense, it is the fraction of the derivative used. This work shows a Bayesian approach to solving this problem with associated simulation studies to illustrate how the method performs on a variety of cases. Extensions to Design of Experiments will be discussed as well.
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