BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

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Matrix Differential Calculus with Applications in Statistics and Econometrics

Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for characterizing such data. This paper proposes a generative mixture-model approach to clustering directional data based on the von Mises-Fisher (vMF) distribution, which arises naturally for data distributed on the unit hypersphere. In particular, we derive and analyze two variants of the Expectation Maximization (EM) framework for estimating the mean and concentration parameters of this mixture. Numerical estimation of the concentration parameters is non-trivial in high dimensions since it involves functional inversion of ratios of Bessel functions. We also formulate two clustering algorithms corresponding to the variants of EM that we derive. Our approach provides a theoretical basis for the use of cosine similarity that has been widely employed by the information retrieval community, and obtains the spherical kmeans algorithm (kmeans with cosine similarity) as a special case of both variants. Empirical results on clustering of high-dimensional text and gene-expression data based on a mixture of vMF distributions show that the ability to estimate the concentration parameter for each vMF component, which is not present in existing approaches, yields superior results, especially for difficult clustering tasks in high-dimensional spaces.

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Clustering on the Unit Hypersphere using von Mises-Fisher Distributions

THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton University Press; London: Oxford University Press, 1941.) 36s. net.

The Laplace Transform

Here are two books on a topic new to Technometrics: statistical and mathematical demography. The first author of Applied Mathematical Demography wrote the first two editions of this book alone. The second edition was published in 1985. Professor Keyfritz noted in the Preface (p. vii) that at age 90 he had no interest in doing another edition; however, the publisher encouraged him to find a coauthor. The result is an additional focus for the book in the world of biology that makes it much more relevant for the sciences. The book is now part of the publisher’s series on Statistics for Biology and Health. Much of it, of course, focuses on the many aspects of human populations. The new material focuses on mature population models, the particular focus of the new author (see, e.g., Caswell 2000). As one might expect from a book that was originally written in the 1970s, it does not include a lot of information on statistical computing. The new book by Alho and Spencer is focused on putting a better emphasis on statistics in the discipline of demography (Preface, p. vii). It is part of the publisher’s Series in Statistics. The authors are both statisticians, so the focus is on statistics as used for demographic problems. The authors are targeting human applications, so their perspective on science does not extend any further than epidemiology. The book actually strikes a good balance between statistical tools and demographic applications. The authors use the first two chapters to teach statisticians about the concepts of demography. The next four chapters are very similar to the statistics content found in introductory books on survival analysis, such as the recent book by Kleinbaum and Klein (2005), reported by Ziegel (2006). The next three chapters are focused on various aspects of forecasting demographic rates. The book concludes with chapters focusing on three areas of applications: errors in census numbers, financial applications, and small-area estimates.

Univariate Discrete Distributions

Multiplicative error accounts for much of the size-scaling and leptokurtosis in fluctuating asymmetry. It arises when growth involves the addition of tissue to that which is already present. Such errors are lognormally distributed. The distribution of the difference between two lognormal variates is leptokurtic. If those two variates are correlated, then the asymmetry variance will scale with size. Inert tissues typically exhibit additive error and have a gamma distribution. Although their asymmetry variance does not exhibit size-scaling, the distribution of the difference between two gamma variates is nevertheless leptokurtic. Measurement error is also additive, but has a normal distribution. Thus, the measurement of fluctuating asymmetry may involve the mixing of additive and multiplicative error. When errors are multiplicative, we recommend computing log E(l) − log E(r), the difference between the logarithms of the expected values of left and right sides, even when size-scaling is not obvious. If l and r are lognormally distributed, and measurement error is nil, the resulting distribution will be normal, and multiplicative error will not confound size-related changes in asymmetry. When errors are additive, such a transformation to remove size-scaling is unnecessary. Nevertheless, the distribution of l − r may still be leptokurtic. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society, 2003, 80, 57–65.

Growth models and the expected distribution of fluctuating asymmetry

This paper provides a regression model in which both covariates and re- sponses are angular variables. The regression curve is expressed as a form of the Mobius circle transformation. The angular error is assumed to follow a wrapped Cauchy or, equivalently, circular Cauchy distribution. A bivariate circular distribu- tion is proposed to model our circular regression. Some properties of the regression, including estimation and testing procedures, are obtained. The proposed methods are applied to marine biology and wind direction data.

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A circular-circular regression model

Melanoma is a skin tumor with high malignancy. Cases of melanoma have recently been reported from many hospitals around the world. Since melanoma is analogous with benign nevus, discriminating between melanoma and benign nevus is difficult for nonspecialists. A screening system for melanoma and benign nevus is desired. Melanoma is mainly diagnosed by features of specific shape and color. However, texture patterns within the tumor region can be diagnostically important. The purpose of this research was to classify patterns on the tumor surface. Digital images of a tumor were classified into 3 patterns by texture analysis: homogeneous pattern; globular pattern; and reticular pattern. The tumor part in the image was specified first, and the specified tumor part was divided into sub-images. Texture features of each sub-image were then calculated. Patterns were classified by discriminant analysis based on the number of texture features. As a result, patterns could be classified correctly into the three categories at a ratio of 94%. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Pattern Classification of Nevus with Texture Analysis

It is known that von Mises-Fisher or Langevin distributions have some analogous properties to multivariate normal distributions and are generated through conditioning suitable multivariate normal distributions. In this paper a new distribution on the unit sphere of arbitrary dimension, which is called the Pearson type VII distribution on the unit sphere, is obtained by conditioning scale mixtures of normal distributions with gamma weight and some properties of the proposed distribution are studied. A special case of the Pearson type VII disitribution on the unit sphere, which is called the t-distribution with n degrees of freedom on the unit sphere in this paper, converges to the von Mises-Fisher distribution as n tends to infinity. The situation is analogous to that of multivariate Student t- and normal distributions in Euclidean space. A new measure of similarity on spheres is also proposed.

Kunio Shimizu

Papers

Growth models and the expected distribution of fluctuating asymmetry

A circular-circular regression model

Pattern Classification of Nevus with Texture Analysis

Pearson type vii distributions on spheres

Dependent models for observations which include angular ones