Physical Sciences and Mathematics Commons^™

Estimation Of The Parameters In A Spatial Regressive-Autoregressive Model Using Ord's Eigenvalue Method, Sajib Mahmud Mahmud Tonmoy

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we study one of Ord's (1975) global spatial regression models.

Ord considered spatial regressive-autoregressive models to describe the interaction

between location and a response variable in the presence of several covariates. He also

developed a practical estimation method for the parameters of this regression model

using the eigenvalues of a weight matrix that captures the contiguity of locations.

We review the theoretical aspects of his estimation method and implement it in the

statistical package R.

We also implement Ord's methods on the Columbus, Ohio, crime data set from the

year 1980, which involves the crime rate of …

Probabilistic Interpretation Of Solutions Of Linear Ultraparabolic Equations, Michael D. Marcozzi

Mathematical Sciences Faculty Research

We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.

Conformal Mapping Improvement Of The Boundary Element Method Solution For Underground Water Flow In A Domain With A Very Singular Boundary, Megan Romero

UNLV Theses, Dissertations, Professional Papers, and Capstones

Numerical solutions using a Boundary Element Method (BEM) for a confined flow in a very singular finite domain are developed. Typically, in scientific journal publications, authors avoid domains with many and more malignant singularities due to the extremely big and difficult to estimate errors in the numerical calculations. Using exact Conformal Mapping solutions for simplified domains with the same singularity as in the original domain, this problem can be solved numerically with improvements introduced by Conformal Mapping solutions. Firstly, to experiment with improving the BEM solution by Conformal Mapping, a domain inside a rectangle is considered. The exact solution inside …

Fundamental Tradeoffs In Estimation Of Finite-State Hidden Markov Models, Justin Le

UNLV Theses, Dissertations, Professional Papers, and Capstones

Hidden Markov models (HMMs) constitute a broad and flexible class of statistical models that are widely used in studying processes that evolve over time and are only observable through the collection of noisy data. Two problems are essential to the use of HMMs: state estimation and parameter estimation. In state estimation, an algorithm estimates the sequence of states of the process that most likely generated a certain sequence of observations in the data. In parameter estimation, an algorithm computes the probability distributions that govern the time-evolution of states and the sampling of data. Although algorithms for the two problems are …