JEM N. CORCORAN 

Controlled accuracy Gibbs sampling of order-constrained non-iid ordered random variates

Published: October, 2022

Order statistics arising from m independent but not identically distributed random variables are typically constructed by arranging some X1,X2,…,Xm, with Xi having distribution function Fi(x), in increasing order denoted as X(1)≤X(2)≤…≤X(m). In this case, X(i) is not necessarily associated with Fi(x). Assuming one can simulate values from each distribution, one can generate such ``non-iid" order statistics by simulating Xi from Fi, for i=1,2,…,m, and simply putting them in order. In this paper, we consider the problem of simulating ordered values X(1),X(2),…,X(m) such that the marginal distribution of X(i) is Fi(x). ...This problem arises in Bayesian principal components analysis (BPCA) where the Xi are ordered eigenvalues that are a posteriori independent but not identically distributed. In this paper, we propose a novel {\emph{coupling-from-the-past}} algorithm to ``perfectly" (up to computable order of accuracy) simulate such "order-constrained non-iid" order statistics. We demonstrate the effectiveness of our approach for several examples, including the BPCA problem.

Rare Events via Cross-Entropy Population Monte Carlo

Published: December 2021

Rare events are events that happen with very low frequency. Estimating rare event probabilities using Monte Carlo techniques is computationally expensive, often to the point of intractability, and special methods are required. Importance sampling (IS) is a well known technique that uses a proposal distribution in place of a target distribution to lower the variance of the estimator. Key to the success of IS methods is the choice of a proposal distribution, or the parameters governing the distribution. Adaptive importance sampling improves the parameters of a family or population of proposal distributions iteratively through trials. ... We present a novel cross-entropy population Monte Carlo algorithm, which adapts the parameters of proposals through the cross-entropy method. The proposed method stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on rare event examples show that the algorithm can outperform existing resampling based population Monte Carlo methods, especially for higher-dimensional problems. We also demonstrate efficacy on a conjunction analysis problem.

Bayesian Fusion of Data Partitioned Particle Estimates

Submitted: October 2020

We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model parameters through Monte Carlo methods, followed by an update and resample scheme related to multiple importance sampling to combine information from the initial estimates. We show the method is convergent in the particle limit and directly suited to application on multi-sensor data fusion problems by demonstrating efficacy on a multi-sensor Keplerian orbit determination problem and a bearings-only tracking problem.

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Earlier Students

10 Ph.D. students in academia, 5 Ph.D. students in national labs, 2 Ph.D. students and 5 M.S. students in industry

Mathematical Statistics • Markov Processes • Measure Theoretic Probability • Stochastic Simulation • Stochastic Differential Equations • Bayesian Statistics • Applied Analysis • Time Series