This article describes a versatile approach to non-linear, non-Gaussian noise target tracking which makes use of both parametric and non-parametric techniques within a Bayesian framework. It produces a Gaussian mixture model (GMM) of a track, but resorts to a sampling technique within the tracking process to handle non-linearity. GMMs are recovered from samples using the expectation-maximisatio...

This work surveys mathematical foundations of Model Order Reduction (MOR for short) techniques in accelerating computational forward and inverse UQ. Operator equations (comprising elliptic and parabolic Partial Differential Equations (PDEs for short) and Boundary Integral Equations (BIEs for short)) with distributed uncertain input, being an element of an infinitedimensional, separable Banach s...

Electrical Engineering) Non-parametric Bayesian Learning with Incomplete Data by Chunping Wang Department of Electrical and Computer Engineering Duke University

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a ran...

Consider the simple setting of point exposure, outcome and confounding variables, all of which are discrete. As is well known, parametric modeling of outcome given exposure and confounders and also exposure given confounders can yield a double-robust estimator. This has the property of being consistent as long as at least one of the two specified models is correct. Such an estimator can also be...

A Bayesian non-parametric approach for efficient risk management is proposed. A dynamic model is considered where optimal portfolio weights and hedging ratios are adjusted at each period. The covariance matrix of the returns is described using an asymmetric MGARCH model. Restrictive parametric assumptions for the errors are avoided by relying on Bayesian nonparametric methods, which allow for a...

We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain Monte Carlo to move between solutions. In contrast, we assume that the number of hidden causes is unbounded, but only a finite number influence observable varia...

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specificall...

To provide insight into patient-level disease dynamics from data collected at irregular time intervals, this work extends applications of semi-parametric clustering for temporal mining. In the semi-parametric clustering framework, Markovian models provide useful parametric assumptions for modeling temporal dynamics, and a non-parametric method is used to cluster the temporal abstractions instea...

Recently, quantile regression (QR) models are often applied for longitudinal data analysis. When the distribution of responses seems to be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. In this paper, a semi-parametric quantile regression model is developed for analysing continuous longitudinal responses. The error term's distribution is assumed to be Asymmetr...