In this paper, a novel methodology for state estimation of stochastic dynamical systems is proposed. In this formulation, finite-term Karhunen-Loève (KL) expansion is used to approximate the process noise, thus resulting in a non-autonomous deterministic approximation (with parametric uncertainty) of the original stochastic nonlinear system. It is proved that the solutions of the approximate dy...

This dissertation introduces a method for predicting the performance of a radiometer design based on calculating the measurement uncertainty. The variety in radiometer designs and the demand for improved radiometric measurements justify the need for a more general and comprehensive method to assess system performance. Radiometric resolution, or sensitivity, is a figure of merit that has been co...

Carbon accounting is at the heart of efforts to mitigate the effects of climate change. One approach for estimating population parameters for live tree stem carbon entails three primary steps: (1) construction of an individual tree, allometric carbon model, (2) application of the model to tree-level data for a probability sample of plots, and (3) use of a probability-based (design-based) estima...

We present numerical methods for computing the Schatten p-norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental design inverse problems, where defines a measure uncertainty. Computing high-dimensional matrices is computationally expensive. propose matrix-free method to estimate using Monte Carlo estimator derive convergence result...

The solution to partial differential equations generally requires approximations that result in numerical error in the final solution. Of the different types of numerical error in a solution, discretization error is the largest and most difficult error to estimate. In addition, the accuracy of the discretization error estimates relies on the solution (or multiple solutions used in the estimate)...

inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...

A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is the point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not an inner product space and conventional Bayes estimators therefore stand without their usual decision theoretic foundation. W...

Regional flood frequency analysis is a convenient way to reduce estimation uncertainty when few data are available at the gauging site. In this work, a model that allows a non null probability to a regional fixed shape parameter is presented. This methodology is integrated within a Bayesian framework and uses reversible jump techniques. The performance on stochastic data of this new estimator i...