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The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the co ...
Shannon's sampling theorem for bandlimited signals, formulated in 1949, has become a cornerstone for modern digital communications and signal processing. The importance of sampling and reconstruction of analog signals has led to great advances in the field ...
We study the problem of learning unknown parameters of stochastic dynamical models from data. Often, these models are high dimensional and contain several scales and complex structures. One is then interested in obtaining a reduced, coarse-grained descript ...
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the im ...
Elevated nitrate from human activity causes ecosystem and economic harm globally. The factors that control the spatiotemporal dynamics of riverine nitrate concentration remain difficult to describe and predict. We analyzed nitrate concentration from 4450 s ...
In this dissertation, I develop theory and evidence to argue that new technologies are central to how firms organize to create and capture value. I use computational methods such as reinforcement learning and probabilistic topic modeling to investigate thr ...
Low-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spa ...
Objective. To study the neural control of movement, it is often necessary to estimate how muscles are activated across a variety of behavioral conditions. One approach is to try extracting the underlying neural command signal to muscles by applying latent ...
The LHCb VELO Upgrade I, currently being installed for the 2022 start of LHC Run 3, uses silicon microchannel coolers with internally circulating bi-phase CO2 for thermal control of hybrid pixel modules operating in vacuum. This is the largest scale applic ...
This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP).The first hierarchical method we present is based ...