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Type: thesis. Topic: Statistic and Mathematic. Code: stat0027.
Format: pdf. Pages: 34

A Comparison of Bayesian Regression Models Applied in Knot Theory

This thesis explores variations on a Bayesian regression model used to estimate the mean box length of a random knot as a function of the number of edges of that knot. Specifically, this research recongizes uncertainty in box length variance and compares the resulting inference with that based on an approach that does not recognize such uncertainty. The Bayesian model is then shown to allow straightforward inference on the crossing location of two population regression lines.

Keywordws: Bayesian | Regression | Model | Knot | Theory

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Type: thesis. Topic: Statistic and Mathematic. Code: stat0028.
Format: pdf. Pages: 62

A Finite Element Approach to Model Electromagnetic Fields Scattered by a Buried Cavity

This research investigates the plane-wave scattering from a two-dimensional arbitrarily shaped cavity embedded in an infinite metallic surface that has been covered with a layer or layers of dielectric material, considering both transverse electric and transverse magnetic polarizations. Due to the shape of the cavity, this problem is approached using the finite element method. This approach provides a boundary condition at the opening of the cavity which accounts for the effect of the overlayer(s) while confining the problem to the finite domain of the cavity itself. After determination of the solution for the electric and magnetic fields at the cavity aperture, the strength of the return echo can then be calculated and displayed in a radar cross section. In addition, numerical verifications and experiments illustrating the efficacy of the approach will be provided by comparison to other previously tested methods.

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Type: thesis. Topic: Statistic and Mathematic. Code: stat0029.
Format: pdf. Pages: 81

A Fourier Solution for Electromagnetic Scattering by a Covered Rectangular Cavity

This research investigates the plane-wave scattering from a two-dimensional rectangular cavity embedded in an infinite metallic surface that has been covered with a dielectric material. The transverse magnetic and transverse electric polarizations are both considered. The rectangular geometry of the embedded cavity allows for the use of a Fourier based solution. Presented here are modifications to the Fourier solution due to the addition of the material layer above the metallic surface. Applying these modifications allows for a solution to be determined for the electric and magnetic fields at the cavity aperture, where the strength of the return echo is then calculated and displayed in a radar cross section. In addition, an alternate method is introduced to improve upon the speed that it takes to determine a solution, providing a close approximation to the actual results.

Keywordws: Electromagnetic | Scattering | Rectangular | Cavity

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Type: thesis. Topic: Statistic and Mathematic. Code: stat0030.
Format: pdf. Pages: 32

A Piecewise Linear Generalized Poisson Regression Approach to Modeling Longitudinal Frequency Data

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Type: term paper. Topic: Statistic and Mathematic. Code: stat0009.
Format: pdf. Pages: 10

Algebraic Connectivity and Degree Sequences of Trees

We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on non-pendant vertices starting at the characteristic set of the Fiedler vector.

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Type: term paper. Topic: Statistic and Mathematic. Code: stat0026.
Format: pdf. Pages: 44

An Analysis of the Distribution of Numbers of the Form axby

This thesis will provide an analysis of the sequences formed in an interspersion. It is known that interspersions can be generated entirely from two infinite sequences of positive integers. Since these sequences are based on the integer parts of multiples of an irrational number, finding an expression for one is equivalent to finding an expression for the other. We shall see that sums involving the floor of an integer multiple of an irrational number 0 can be evaluated by first expressing the indices of a summation in the numeration system based on the denominators of the convergents of 0. We shall then turn our attention towards counting the number of times a particular element appears in some sequence G. It will be shown that a minimum of two repetition lengths occur.

Keywordws: Beatty Sequence | Characteristic Sequence | Sturmian Sequence

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Type: term paper. Topic: Statistic and Mathematic. Code: stat0012.
Format: pdf. Pages: 9

Approximate replication of high-breakdown robust regression techniques

This paper demonstrates that even regression results obtained by techniques close to the standard ordinary least squares (OLS) method can be difficult to replicate if a stochastic model fitting algorithm is employed.

Keywordws: robust regression | least squares | replication | stochastic algorithm

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Type: term paper. Topic: Statistic and Mathematic. Code: stat0007.
Format: pdf.

Automatic generation of simple (statistical) exams

Package exams provides a framework for automatic generation of simple (statistical) exams. To employ the tools, users just need to supply a pool of exercises and a master file controlling the layout of the final PDF document. The exercises are specified in separate Sweave files (containing R code for data generation and LaTeX code for problem and solution description) and the master file is a LaTeX document with some additional control commands. This paper gives an overview on the main design aims and principles as well as strategies for adaptation and extension. Hands-on illustrations - based on example exercises and control files provided in the package - are presented to get new users started easily.

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Type: term paper. Topic: Statistic and Mathematic. Code: stat0021.
Format: pdf. Pages: 13

Automatic Random Variate Generation for Unbounded Densities

A new automatic algorithm for sampling from monotone, unbounded densities is presented. The user has to provide a program to evaluate the density and its derivative and the location of the pole. Then the setup of the new algorithm constructs different hat functions for the pole region and for the tail region, respectively. For the pole region a new method is developed that uses a transformed density rejection hat function of the inverse density. As the order of the pole is calculated in the setup, conditions that guarantee the correctness of the constructed hat functions are provided. Numerical experiments indicate that the new algorithm works correctly and moderately fast for many different unbounded densities. The proposed algorithm is the first black-box method that works for unbounded densities suggested in the literature.

Keywordws: non-uniform random variates | universal method | black-box algorithm | transformed density rejection

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Type: thesis. Topic: Statistic and Mathematic. Code: stat0031.
Format: pdf. Pages: 29

Bayesian Analysis of Discrete Longitudinal Data

This thesis explores a Bayesian hierarchical model to compare treatment e®ectiveness for menopausal symptom relief. Speci¯cally, this model recognizes the discrete nature of the data, as well as its time dependency. Bayesian analisys is used to make inference on each individual pro¯le, as well as on a group pro¯le for each treatment group.

Keywordws: Bayesian Analysis | Discrete Longitudinal

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