Statistical Theory Commons^™

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

Marginal Regression Of Gaps Between Recurrent Events, Yijian Huang, Ying Qing Chen

U.C. Berkeley Division of Biostatistics Working Paper Series

Recurrent event data typically exhibit the phenomenon of intra-individual correlation, owing to not only observed covariates but also random effects. In many applications, the population can be reasonably postulated as a heterogeneous mixture of individual renewal processes, and the inference of interest is the effect of individual-level covariates. In this article, we suggest and investigate a marginal proportional hazards model for gaps between recurrent events. A connection is established between observed gap times and clustered survival data, however, with informative cluster size. We then derive a novel and general inference procedure for the latter, based on a functional formulation of …

Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch

U.C. Berkeley Division of Biostatistics Working Paper Series

The pool-adjacent violator-algorithm (Ayer, et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters. By making use of variants of the pool adjacent violator algorithm, we obtain a simple algorithm to compute the maximum likelihood estimator and demonstrate …

Statistical Inference For Simultaneous Clustering Of Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Current methods for analysis of gene expression data are mostly based on clustering and classification of either genes or samples. We offer support for the idea that more complex patterns can be identified in the data if genes and samples are considered simultaneously. We formalize the approach and propose a statistical framework for two-way clustering. A simultaneous clustering parameter is defined as a function of the true data generating distribution, and an estimate is obtained by applying this function to the empirical distribution. We illustrate that a wide range of clustering procedures, including generalized hierarchical methods, can be defined as …

N-Player Prisoner's Dilemma In Multiple Groups: A Model Of Multilevel Selection, Jeffrey Fletcher, Martin Zwick

Complex Systems Faculty Publications and Presentations

This presentation discusses simulations of the n-player Prisoner's Dilemma in populations consisting of multiple groups, and how Sampson's paradox can emerge in such game theoretic situations.

How Do Judges Think About Risk?, W. Kip Viscusi

Vanderbilt Law School Faculty Publications

A sample of almost 100 judges exhibited well-known patterns of biases in risk beliefs and reasonable implicit values of life. These biases and personal preferences largely do not affect attitudes toward judicial risk decisions, though there are some exceptions, such as ambiguity aversion, misinterpretation of negligence rules, and retrospective risk assessments in accident cases, which is a form of hindsight bias. Although judges avoided many pitfalls exhibited by jurors and the population at large, they nevertheless exhibited systematic errors, particularly for small probability-large loss events. These findings highlighted the importance of judicial review and the input of expert risk analysts …

Assessing The Accuracy Of A New Diagnostic Test When A Gold Standard Does Not Exist, Todd A. Alonzo, Margaret S. Pepe

UW Biostatistics Working Paper Series

Often the accuracy of a new diagnostic test must be assessed when a perfect gold standard does not exist. Use of an imperfect test biases the accuracy estimates of the new test. This paper reviews existing approaches to this problem including discrepant resolution and latent class analysis. Deficiencies with these approaches are identified. A new approach is proposed that combines the results of several imperfect reference tests to define a better reference standard. We call this the composite reference standard (CRS). Using the CRS, accuracy can be assessed using multistage sampling designs. Maximum likelihood estimates of accuracy and expressions for …

Comparison Of Median Indicator Kriging With Full Indicator Kriging In The Analysis Of Spatial Data, Donna Hill

Theses : Honours

In the earth sciences, and particularly in the mining of precious metals, data distributions are often strongly positively skewed. When making decisions on the potential profitability of a gold mine, for example, the high values of the distribution are of particular importance. Indicator kriging provides estimates of cumulative distribution functions from which grade tonnage curves may be calculated. Multiple or full indicator kriging requires a semivariogram to be modelled and a kriging system of equations to be solved for each cut off. This can be time consuming and modelling indicator semivariograms at high cut-offs may be difficult because of the …

Design And Statistical Analysis Of Plant Protection Experiment, J F. Wallace

All other publications

An Australian co-operation with the national agricultural research project Thailand.

This short course is intended to cover aspects of experimental design, sampling and statistical analysis for researchers in Entomology and Plant Pathology.

The basic principles of experimental design are the same for plant protection research as they are in other areas of research. Problems in plant protection arise from the variation of the data, the complexity of the systems and interactions with environmental factors. In many cases, standard designs are quite adequate.

Statistical Calibration Theory, James John Mckeon

Mathematics & Statistics Theses & Dissertations

A calibration method substitutes for measurements, X(,i), that are accurate but impractical or costly, a set of measurements, Y(,i), that are less accurate but simpler or less costly. There are two general types of calibration methods. The classical approach in which once the calibration sample is drawn, the estimates of the X values for a given unit is found without any consideration of the distribution of X values for the other units to be measured. This corresponds best to the literal meaning of the word "calibration". Maximum likelihood estimation is the statistical formulation of the classical approach.

The second approach …

A Computerized Demonstration Of The Central Limit Theorem In Statistics, Paul S. T. Lee

Publications

The Central Limit Theorem is one of the most important concepts in statistics. It provides a link between sample statistics and population parameters. It is a basic concept for understanding various hypothesis-testing techniques such as Student's t-distribution, x²-distribution and F-distribution.

Simulation Of Mathematical Models In Genetic Analysis, Dinesh Govindal Patel

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In recent years a new field of statistics has become of importance in many branches of experimental science. This is the Monte Carlo Method, so called because it is based on simulation of stochastic processes. By stochastic process, it is meant some possible physical process in the real world that has some random or stochastic element in its structure. This is the subject which may appropriately be called the dynamic part of statistics or the statistics of "change," in contrast with the static statistical problems which have so far been the more systematically studied. Many obvious examples of such processes …

History And Proof Of The Binomial Theorem, Ethel B. Ray

Bachelors’ Theses

Everyone realizes what a wonderful place the world really is. Yet, we of this day little think of the many generations that have gone to make our universe as it is. We think we have done wonders. We pride ourselves on our modern way. There is a tendency in man to "pat himself on the back" and boast of how well he has done. Little do we realize that millions and millions of people have given their whole lives so that we might be as we are. Of course the soldier gives his life for his country; but what of …