Probability Commons^™

On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su

All HMC Faculty Publications and Research

When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.

Multi-Level Decomposition Of Probalistic Relations, Stanislaw Grygiel, Martin Zwick, Marek Perkowski

Systems Science Faculty Publications and Presentations

Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way so as to minimize a cost function which depends on the size and structure of the result. The decomposition is repeated iteratively until a stopping criterion is met. Topology and contents of the resulting structure develop dynamically in the decomposition process and reflect relationships hidden in the data.

Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan

Mathematics Faculty Research Publications

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this signi cantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.

Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny

Doctoral Dissertations

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …

Using Simulated Annealing In Geostatistics, Wesley Wells

Theses : Honours

Simulation methods are now used extensively for estimation and prediction in mining and petroleum industries and also in environmental management. In this thesis we describe the method of simulated annealing and examine in detail the GSLIB implementation algorithm SASJM. In the context of two case studies involving both sample and exhaustive data sets, we demonstrate this algorithm and then investigate the effect on the outcome of varying the different algorithm parameters. We also consider the effect of varying the weighting given in the simulated annealing objective function to the reproduction of each of the sample histogram and semivariogram. For the …