Statistics and Probability Commons^™

Optimal Path Planning And The Fast Marching Method, J. J. Clark

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The problem of determining an optimal path for an object moving through some obstacle space presents several nontrivial subproblems. The foremost being the computational complexity that is involved and how to best deal with the associated large data volume. For example, a non-symmetric object moving in three dimensions possesses six degrees of freedom. This can lead to a computational grid that may easily be on the order of 10¹². Furthermore, for every point in the computational domain, several complex calculations must be performed. These include performing tests to determine if the object and obstacles intersect, and numerically solving …

Clinically Relevant Aspects Of Chronic Pain: Normal Personality Predictors, Stephen Ray Nitch

Loma Linda University Electronic Theses, Dissertations & Projects

This study examined the normal personality characteristics of chronic pain patients using cluster analysis. To date, much of the research involving chronic pain and personality has assumed that signs of psychopathology are likely to be present (Jay, Grove, and Grove, 1987; Love and Peck, 1987). There have been some exceptions to this trend by researchers who sought to measure the normal personality structure of individuals with chronic pain (see Wade, Dougherty, Hart, and Cook, 1992). One of central aims of the current study was to further refine the psychosocial taxonomy of chronic pain patients by paying more attention to individual …

Il-10 And Alveolar Bone Loss, Abdulaziz Saud Al-Rasheed

Loma Linda University Electronic Theses, Dissertations & Projects

Interleukin-10 (IL-10) is a cytokine with anti-inflammatory activities. IL-10 knockout (KO) mice exhibit severe intestinal inflammation in the presence of normal gut flora. We hypothesized that IL-10 KO mice would also be susceptible to inflammatory periodontal disease resulting in alveolar bone loss (ABL). The purpose of this study was to compare naturally occurring ABL in IL-10 KO and wild type (WT) mice. Twelve IL-10 KO and 12 WT mice, age-(7 months) and sex-(male) matched, were used. Half of the mice were on 129/SvEv and half on C57BL/6J background. Animal heads were defleshed and treated to remove all organic material. ABL …

Visualization Methods: A Comparative Study Of New, Traditional And Robust Procedures, Kimberly Crimin

Dissertations

Two major goals in discriminant analysis are discrimination and classification. In discrimination, the goal is to describe graphically (visualization) different features of several known groups. In classification, the goal is to allocate unknown observations to one of several known groups. We have developed new visualization procedures based on traditional estimating procedures and also on robust estimating procedures. We have further developed robust classification procedures. We propose several robust classification procedures based on coordinatewise and affine equivariant, rank-based robust estimates. Empirical studies are performed over many different error distributions. These studies result in empirical efficiencies of the robust and traditional procedures. …

Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern

Mathematics and Statistics Faculty Publications

Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of …

Nearly Balanced And Resolvable Block Designs, Brian Henry Reck

Mathematics & Statistics Theses & Dissertations

One of the fundamental principles of experimental design is the separation of heterogeneous experimental units into subsets of more homogeneous units or blocks in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given v treatments to compare, and having available b blocks of k experimental units each, the thoughtful statistician asks, “What is the optimal allocation of the treatments to the units?” This is the basic block design problem. Let n_ij be the number of times treatment i is used in block j and let N be the v x b matrix N …

Autoassociative-Heteroassociative Neural Network, Claudia V. Kropas-Hughes, Steven K. Rogers, Mark E. Oxley, Matthew Kabrisky

AFIT Patents

An efficient neural network computing technique capable of synthesizing two sets of output signal data from a single input signal data set. The method and device of the invention involves a unique integration of autoassociative and heteroassociative neural network mappings, the autoassociative neural network mapping enabling a quality metric for assessing the generalization or prediction accuracy of the heteroassociative neural network mapping.

Trial Outcomes And Demographics: Is There A Bronx Effect?, Theodore Eisenberg, Martin T. Wells

Cornell Law Faculty Publications

Minorities favor injured plaintiffs and give them inflated awards. This folk wisdom in the legal community influences choice of trial locale and the screening of jurors. A Los Angeles court is said to be known by local lawyers as "the bank" because of the frequency and size of its anti-corporate awards. A newspaper article summarizing court results suggests, somewhat jokingly, that the "Bronx County Courthouse should post a warning: People who get sued here run an increased risk of suffering staggering losses." Beliefs about the influence of factors other than race, such as income and urbanization, also are common.

This …

Reconciling Experimental Incoherence With Real-World Coherence In Punitive Damages, Theodore Eisenberg, Jeffrey J. Rachlinski, Martin T. Wells

Cornell Law Faculty Publications

Experimental evidence generated in controlled laboratory studies suggests that the legal system in general, and punitive damages awards in particular, should display an incoherent pattern. According to the prediction, inexperienced decisionmakers, such as juries, should fail to convert their qualitative judgments of defendants' conduct into consistent, meaningful dollar amounts. This Article tests this prediction and finds modest support for the thesis that experience across different types of cases will lead to greater consistency in awards. Despite this support, numerous studies of damage awards in real cases detect a generally sensible pattern of damage awards. This Article tries to reconcile the …

Nonlinear Regression Based On Ranks, Asheber Abebe

Dissertations

This study presents robust methods for estimating parameters of nonlinear regression models. The proposed methods obtain estimates by minimizing rankbased dispersions instead of the Euclidean norm. We focus on the Wilcoxon and generalized signed-rank dispersion functions. Asymptotic properties of the estimators are established under mild regularity conditions similar to those used in least squares and least absolute deviations estimation. The study also shows that by considering the generalized signed-rank dispersion we obtain a class of estimators that encompasses most of the existing popular nonlinear regression estimators. As in linear models, these rank-based procedures provide estimators that are highly efficient. This …

Inference For Proportional Mean Residual Life Model In The Presence Of Censoring, Ying Q. Chen, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

As a function of time t, mean residual life is defined as remaining life expectancy of a subject given its survival to t. It plays an important role in many research areas to characterise stochastic behavior of survival over time. Similar to the Cox proportional hazard model, the proportional mean residual life model were proposed in statistical literature to study association between the mean residual life and individual subject's explanatory covariates. In this article, we will study this model and develop appropriate inference procedures in presence of censoring. Numerical studies including simulation and real data analysis are presented as well.

Power Analyses When Comparing Trimmed Means, Rand R. Wilcox, H. J. Keselman

Journal of Modern Applied Statistical Methods

Given a random sample from each of two independent groups, this article takes up the problem of estimating power, as well as a power curve, when comparing 20% trimmed means with a percentile bootstrap method. Many methods were considered, but only one was found to be satisfactory in terms of obtaining both a point estimate of power as well as a (one-sided) confidence interval. The method is illustrated with data from a reading study where theory suggests two groups should differ but nonsignificant results were obtained.

Some Locally Most Powerful Rank Tests For Correlation, W. J. Conover

Journal of Modern Applied Statistical Methods

Four examples are given to illustrate the ease and practicality of the procedure for finding locally most powerful rank tests for correlation. The first two examples deal with bivariate exponential models. The third example uses the bivariate normal distribution, and the fourth example analyzes the Morgenstem’s general correlation model.

Exact Level And Power Of Permutation, Bootstrap, And Asymptotic Tests Of Trend, Christopher D. Corcoran, Cyrus R. Mehta

Journal of Modern Applied Statistical Methods

We develop computational tools that can evaluate the exact size and power of three tests of trend (e.g., permutation, bootstrap and asymptotic) without resorting to large-sample theory or simulations. We then use these tools to compare the operating characteristics of the three tests. It is seen that the bootstrap test is ultra-conservative relative to the other two tests and as a result suffers from a severe deterioration in power. The power of the asymptotic test is uniformly larger than that of the other two tests, but it fails to preserve the Type I error for most of the range of …

Six Modifications Of The Aligned Rank Transform Test For Interaction, Kathleen Peterson

Journal of Modern Applied Statistical Methods

Testing for interactions in multivariate experiments is an important function. Studies indicate that much data from social studies research is not normally distributed, thus violating that assumption of the AN OVA procedure. The aligned rank transformation test (ART), aligning using the means of columns and rows, has been found, in limited situations, to be robust to Type I error rates and to have greater power than the ANOVA. This study explored a variety of alignments, including the median, Winsorized trimmed means (10%) and (20%), the Huber_1.28 M-estimator, and the Harrell-Davis estimator of the median. Results are reported for Type …

Two Methods To Estimate Homogenous Markov Processes, Ricardo Ocaña-Rilola

Journal of Modern Applied Statistical Methods

Multi-state Markov processes have been introduced recently in Health Sciences in order to study disease history events. This sort of model have some advantages respect to traditional survival analysis, therefore they are an important line of research into stochastic processes applied to Epidemiology. However these types of models increase the complexity of analysis, even for simpler processes, and standard software is limited. In this paper, two methods for fitting homogeneous Markov models are proposed and compared.

The Trouble With Trivials (P > .05), Shlomo S. Sawilowsky, Jina S. Yoon

Journal of Modern Applied Statistical Methods

Trivials are effect sizes associated with statistically non-significant results. Trivials are like Tribbles in the Star Trek television show. They are cute and loveable. They proliferate without limit. They probably growl at Bayesians. But they are troublesome. This brief report discusses the trouble with trivials.

An Error In Statistical Logic In The Application Of Genetic Paternity Testing, Ernest P. Chiodo, Joseph L. Musial, J. Sia Robinson

Journal of Modern Applied Statistical Methods

A Bayes probability computer program was written in Fortran to examine issues related to genetic paternity testing. An application was given to demonstrate the effects improper assumptions of prior probability of culpability. The seriousness of such errors include the potential of assigning paternity to wrongly accused men, or wrongly refuting paternity.

An Adaptive Inference Strategy: The Case Of Auditory Data, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

By way of an example some of the basic features in the derivation and use of adaptive inferential methods are demonstrated. The focus of this paper is dyadic (coupled) data in auditory and perceptual research. We present: (a) why one should not use the conventional methods, (b) a derivation of an adaptive method, and (c) how the new adaptive method works with the example data. In the concluding remarks we draw attention to the work of Professor George Barnard who provided the adaptive inference strategy in the context of the Behrens-Fisher problem -- testing the equality of means when one …

Parametric Analyses In Randomized Clinical Trials, Vance W. Berger, Clifford E. Lunneborg, Michael D. Ernst, Jonathan G. Levine

Journal of Modern Applied Statistical Methods

One salient feature of randomized clinical trials is that patients are randomly allocated to treatment groups, but not randomly sampled from any target population. Without random sampling parametric analyses are inexact, yet they are still often used in clinical trials. Given the availability of an exact test, it would still be conceivable to argue convincingly that for technical reasons (upon which we elaborate) a parametric test might be preferable in some situations. Having acknowledged this possibility, we point out that such an argument cannot be convincing without supporting facts concerning the specifics of the problem at hand. Moreover, we have …

Alternatives To SW In The Bracketed Interval Of The Trimmed Mean, Jennifer Bunner, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The aim of this Monte Carlo study is to examine alternatives to estimated variability in building bracketed intervals about the trimmed mean.

Generation Of Combinations Using Excel, Constantine Stamatopoulos

Journal of Modern Applied Statistical Methods

Theoretical development of combinations via enumeration methods are considered. An Excel macro is provided.

Jmasm1: Rangen 2.0 (Fortran 90/95), Gail F. Fahoome

Journal of Modern Applied Statistical Methods

Rangen 2.0 is Fortran 90 module of subroutines used to generate uniform and nonuniform pseudo-random deviates. It includes uni1, an uniform pseudo-random number generator, and non-uniform generators based on unil. The subroutines in Rangen 2.0 were written using Essential Lahey Fortran 90, a proper subset of Fortran 90. It includes both source code for the subroutines and a short description of each subroutine, its purpose, and the arguments including data type and usage.

Asymptotic And Exact Tests In 2 X C Ordered Categorical Contingency Tables With Statxact 2.0 - 4.0, Margaret Posch

Journal of Modern Applied Statistical Methods

The purpose of this study was to compare the statistical power of a variety of exact tests in the 2 x C ordered categorical contingency table using StatXact software. The Wilcoxon Rank Sum, Expected Nonnal Scores, Savage Scores (or its Log Rank equivalent), and Permutation tests were studied. Results indicated that the procedures were nearly the same in terms of comparative statistical power.

Quantifying Bimodality Part I: An Easily Implemented Method Using Spss, B. W. Frankland, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Scientists in a variety of fields are faced with the question of whether or not a particular sample of data are best described as unimodal or bimodal. We provide a simple and convenient method for assessing bimodality. The use of the non-linear algorithms in SPSS for modeling complex mixture distributions is demonstrated on a unimodal normal distribution (with 2 free parameters) and on bimodal mixture of two normal distributions (with 5 free parameters).

A Measure Of Relative Efficiency For Location Of A Single Sample, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The question of how much to trim or which weighting constant to use are practical considerations in applying robust methods such as trimmed means (L-estimators) and Huber statistics (M-estimators). An index oflocation relative efficiency (LRE), which is a ratio of the narrowness of resulting confidence intervals, was applied to various trimmed means and Huber M-estimators calculated on seven representative data sets from applied education and psychology research. On the basis of LREs, lightly trimmed means were found to be more efficient than heavily trimmed means, but Huber M-estimators systematically produced narrower confidence intervals. The weighting constant of ψ = 1.28 …

Two-Sided Equivalence Testing Of The Difference Between Two Means, R. Clifford Blair, Stephen R. Cole

Journal of Modern Applied Statistical Methods

Studies designed to examine the equivalence of treatments are increasingly common in social and biomedical research. Herein, we outline the rationale and some nuances underlying equivalence testing of the difference between two means. Specifically, we note the odd relation between tests of hypothesis and confidence intervals in the equivalence setting.

Jmasm3: A Method For Simulating Systems Of Correlated Binary Data, Todd C. Headrick

Journal of Modern Applied Statistical Methods

An efficient algorithm is derived for generating systems of correlated binary data. The procedure allows for the specification of all pairwise correlations within each system. Intercorrelations between systems can be specified qualitatively. The procedure requires the simultaneous solution of a system of equations for obtaining the threshold probabilities to generate each system of binary data. A numerical example is provided to demonstrate that the procedure generates correlated binary variables that yield correlations in close agreement with the specified population correlations.

Combining Two Nonparametric Tests Of Location, R. Clifford Blair

Journal of Modern Applied Statistical Methods

A distribution-free test is proposed whose power is similar to that of the Wilcoxon Rank-Sum or Terry-Hoeffding Normal Scores tests depending on which of these two tests is more powerful in a given data analysis situation, regardless of the population. This new statistic is distribution-free, and adds no new assumptions to those associated with the constituent tests. A table of critical values for the new statistic is given and some of its Type I error and power properties are examined.

An Unconditional Exact Test For Small Samples Matched Binary Pairs, Robert A. Malkin

Journal of Modern Applied Statistical Methods

When investigators have N pairs of binary data, a common test for an increased rate of response is McNemar's test. However, McNemar's is an approximate, conditional test. An exact, unconditional test exists, but requires restrictive assumptions. Critical values and power tables are presented for an exact, unconditional test free of these assumptions.