[by] Laszlo Tisza, Paul M. Quay. / Repr. from Annals of physics. v. 25, no. 1. Oct. 1963.

Accident statistics have often been used to support the argument that an abnormally small proportion of drivers account for a large proportion of the accidents. This paper compares statistics developed from six-year data for 7, 800 California drivers with results predicted using compound Poisson models for driver accident involvement that assume specific variations in accident likelihood among drivers. The results indicate that the fraction of drivers accounting for various proportions of all accident involvements is too high to suggest that "chronic" accident repeaters are involved in most accidents. / National Science Foundation under Grants GK- 1685 and GK- 16471

This paper is an example of the growing interface between statistics and mathematical optimization. A very efficient heuristic algorithm for the combinatorially intractable TSP is presented, from which statistical estimates of the optimal tour length can be derived. Assumptions, along with computational experience and conclusions are discussed. / Supported in part by the U.S. Department of Transportation under contract DOT-TSC-1058, Transportation Advanced Research Program (TARP).

I describe an exploration criterion that attempts to minimize the error of a learner by minimizing its estimated squared bias. I describe experiments with locally-weighted regression on two simple kinematics problems, and observe that this "bias-only" approach outperforms the more common "variance-only" exploration approach, even in the presence of noise.

Two formulations of model-based object recognition are described. MAP Model Matching evaluates joint hypotheses of match and pose, while Posterior Marginal Pose Estimation evaluates the pose only. Local search in pose space is carried out with the Expectation--Maximization (EM) algorithm. Recognition experiments are described where the EM algorithm is used to refine and evaluate pose hypotheses in 2D and 3D. Initial hypotheses for the 2D experiments were generated by a simple indexing method: Angle Pair Indexing. The Linear Combination of Views method of Ullman and Basri is employed as the projection model in the 3D experiments.

For many types of learners one can compute the statistically 'optimal' way to select data. We review how these techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate.

<p>Zaykin, Dmitri V. Statistical Analysis of Genetic Associations.Advisor: Bruce S. Weir.There is an increasing need for a statistical treatment of geneticdata prompted by recent advances in molecular genetics and moleculartechnology. Study of associations between genes is one of the mostimportant aspects in applications of population genetics theory andstatistical methodology to genetic data. Developments of these methodsare important for conservation biology, experimental populationgenetics, forensic science, and for mapping human disease genes. Overthe next several years, genotypic data will be collected to attemptlocating positions of multiple genes affecting disease phenotype.Adequate statistical methodology is required to analyze thesedata. Special attention should be paid to multiple testing issuesresulting from searching through many genetic markers and high risk offalse associations. In this research we develop theory and methodsneeded to treat some of these problems. We introduce exact conditionaltests for analyzing associations within and between genes in samplesof multilocus genotypes and efficient algorithms to perform them.These tests are formulated for the general case of multiple alleles atarbitrary numbers of loci and lead to multiple testing adjustmentsbased on the closing testing principle, thus providing strongprotection of the family-wise error rate. We discuss an applicationof the closing method to the testing for Hardy-Weinberg equilibriumand computationally efficient shortcuts arising from methods forcombining p-values that allow to deal with large numbers of loci. Wealso discuss efficient Bayesian tests for heterozygote excess anddeficiency, as a special case of testing for Hardy-Weinbergequilibrium, and the frequentist properties of a p-value type ofquantity resulting from them. We further develop new methods forvalidation of experiments and for combining and adjusting independentand correlated p-values and apply them to simulated as well as toactual gene expression data sets. These methods prove to be especiallyuseful in situations with large numbers of statistical tests, such asin whole-genome screens for associations of genetic markers withdisease phenotypes and in analyzing gene expression data obtained fromDNA microarrays.<P>

<p>This thesis research is motivated by a special type of missing data - Gap Data, which was first encountered in a cardiology study conducted at Duke Medical School. This type of data include multiple observations of certain event time (in this medical study the event is the reopenning of a certain artery), some of them may have one or more missing periods called ``gaps'' before observing the``first'' event. Therefore, for those observations, the observed first event may not be the true first event because the true first event might have happened in one of the missing gaps. Due to this kind of missing information, estimating the survival function of the true first event becomes very difficult. No research nor discussion has been done on this type of data by now. In this thesis, the auther introduces a new nonparametric estimating method to solve this problem. This new method is currently called Imputed Empirical Estimating (IEE) method. According to the simulation studies, the IEE method provide a very good estimate of the survival function of the true first event. It significantly outperforms all the existing estimating approaches in our simulation studies. Besides the new IEE method, this thesis also explores the Maximum Likelihood Estimate in thegap data case. The gap data is introduced as a special type of interval censored data for thefirst time. The dependence between the censoring interval (in the gap data case is the observedfirst event time point) and the event (in the gap data case is the true first event) makes the gap data different from the well studied regular interval censored data. This thesis points of theonly difference between the gap data and the regular interval censored data, and provides a MLEof the gap data under certain assumptions.The third estimating method discussed in this thesis is the Weighted Estimating Equation (WEE)method. The WEE estimate is a very popular nonparametric approach currently used in many survivalanalysis studies. In this thesis the consistency and asymptotic properties of the WEE estimateused in the gap data are discussed. Finally, in the gap data case, the WEE estimate is showed to be equivalent to the Kaplan-Meier estimate. Numerical examples are provied in this thesis toillustrate the algorithm of the IEE and the MLE approaches. The auther also provides an IEE estimate of the survival function based on the real-life data from Duke Medical School. A series of simulation studies are conducted to assess the goodness-of-fit of the new IEE estimate. Plots and tables of the results of the simulation studies are presentedin the second chapter of this thesis.<P>

Statistical modeling with counts of bats

Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.