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A & M Research Statement

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Research Statement
Nilabja Guha Texas A&M University
My current research at Texas A&M University is in a broad area of uncertainty quantification (UQ), with applications to inverse problems, transport based filtering, graphical models and online learning. My research projects are motivated by many real-world problems in engineering and life sciences. In my current postdoctoral position in the Institute for Scientific Computation (ISC) at Texas A&M University, I have worked with Professor Bani K. Mallick from the department of statistics and Professor Yalchin Efendiev from the department of mathematics. I have collaborated with researchers in engineering and bio-sciences on developing rigorous uncertainty quantification methods within the Bayesian …show more content…

In these problems, which arise in many petroleum and hydrology applications, the forward problems are compu- tationally expensive and highly heterogeneous with multiple space and time scales. Developing rigorous uncertainty quantification approaches, which can identify data-relevant scales and entail probabilistic in- terpretation for un-resolved scales is challenging and has been my research goal. On another application in aerospace engineering, my research goal has been developing optimal transport based space situational awareness (SSA) methods to view, understand and predict the physical location of natural and manmade objects in orbit around the Earth, where the main challenges are non–Gaussian distribution, sparsity of observation and, system and observational error. On graphical model related problems, the main focus is on developing robust computationally efficient graph estimation methodology in applications related to determining protein networks. Network estimation methodologies in graphical models depend heavily on the assumptions of Gaussianity and the focus of my work has been on developing robust distribution free approaches. In the online learning application, I have extended a stochastic approximation based predictive recursion algorithm for dependent …show more content…

A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback–Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g., Cauchy problem and permeability estimation problem. The proposed method performs comparably with full Markov chain Monte Carlo (MCMC) in terms of accuracy and is computationally

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