Tarek A. Moselhy

Tarek A. Moselhy
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Tarek A. Moselhy

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Statistics - Computation (3)
Mathematics - Probability (2)
Mathematics - Statistics (1)
Statistics - Theory (1)
Statistics - Applications (1)
Statistics - Methodology (1)
Mathematics - Numerical Analysis (1)

Publications Authored By Tarek A. Moselhy

We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e. Read More

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This work introduces a multiscale decomposition that exploits conditional independence across scales, when present in certain classes of inverse problems, to decouple Bayesian inference into two stages: (1) a computationally tractable coarse-scale inference problem; and (2) a mapping of the low-dimensional coarse-scale posterior distribution into the original high-dimensional parameter space. Read More

We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving map is established by formulating the problem in the context of optimal transport theory. We discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem, exploiting gradient information from the forward model when possible. Read More