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Membership functions characterize fuzzy sets. A calculus for
these functions has been proposed by Zadeh, and has been suggested by him
as an alternative to the
calculus of probability. His claim is that the calculus of
probability is inadequate for describing all types of uncertainty. The
alternative calculus is termed possibily theory. Possibility
Theory has been criticized on grounds that it does not have an
axiomatic foundation based on primitives that are natural.

This talk is in two parts: the first is expository; it overviews fuzzy
sets, membership functions and possibility theory. The second part shows
how membership functions can be used to obtain probability measures of
fuzzy sets. The crux of the idea behind the latter is to conceptualize the
decision maker as probabilist who elicits expert testimony via the
membership function. Our conceptualization makes the process coherent
vis a vis the behaviouristic axioms of Ramsey and Savage.
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TITLE: Mathematical Statistician Positions at the Census Bureau
SPEAKER: Carol Caldwell
Census Bureau
DATE: October 22, 1999
LOCATION: Funger Hall 320
TIME: 11:00 a.m.

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Mathematical statisticians work on a wide variety of interesting projects
at the Census Bureau. This talk will provide a brief overview of what
Census Bureau mathematical statisticians do, and describe the
qualifications needed to join the Census Bureau as a "math stat." The
talk will also describe some of the particular challenges of conducting
surveys of businesses, which the Census Bureau has been doing for many
years.
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TITLE: Stable Distributions: Models for Heavy Tailed Data SPEAKER: John Nolan American University DATE: October 29, 1999 LOCATION: Funger Hall 320 TIME: 11:00 am ------------------------------------------------------------------------- Stable random variables are the r.v.s that retain their shape when added together. These distributions generalize the Gaussian distribution and allow skewness and heavy tails - features found in many large data sets. We give an overview of univariate and multivariate stable laws, focusing on statistical applications. These distributions are now computationally accessible and should be added to the toolbox of the working statistician. -------------------------------------------------------------------------

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TITLE: Some recent developments in the nonparametric estimation with randomly truncated data SPEAKER: Grace L. Yang University of Maryland - College Park DATE: November 5, 1999 LOCATION: Funger 320 TIME: 11:00 am ---------------------------------------------------------------------- Under random truncation, the random variables X and Y are both observable only if X is larger than Y; the type of data occur in astronmy, economics, biometry, reliability and some other fields. In astronomy, the truncation effect is known as the Malmquist bias or the Scott effect in the study of galaxies. In reliablity, X and Y correspond respectively to the stress and strength of a material. In a randomly truncated sample, the proportion of missing observations is unknown. Yet, the estimation of the missing probability $ r = P[X < Y] $ is key to the nonparametric analysis of the data. In this presentation, we discuss a certain estimator of r. We utilize it to study the estimates $T(F_{n})$ of the functionals $T(F)$ of the distsribution function F of X Here $F_{n}$ is the product-limit estimator of F which has been studied systematically by Woodroofe (1985), and many others thereafter. Our estimator of $r$ is also instrumental in regression analysis with truncated data. ----------------------------------------------------------------------

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TITLE: Statistical Methods for Linkage Analysis of Sib Pair Data
SPEAKER: Zhaohai Li
George Washington University
DATE: November 19, 1999
LOCATION: Monroe 104
TIME: 11:00 am

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Sib pair linkage studies are commonly used for the investigating whether
there is a genetic component involved in complex traits. Penrose (1935,
1953) initiated sib pair methods based on the idea that sib pairs with
similar phenotypes have an excess of allele sharing while sib pairs with
dissimilar phenotypes have a deficit of allele sharing. Haseman and Elston
(1972) developed another sib pair method for linkage analysis of
quantitative trait loci (QTL). Risch and Zhang (1995) proposed increasing
the power of tests by focusing on sib pairs with extremely discordant (ED)
or concordant (EC) trait values. We propose more powerful weighted test
statistics than the standard test statistics by using both ED and EC sib
pairs for linkage analysis.

Linkage studies utilizing sib pairs usually assume all sib pairs are full
sibs. Some of these pairs, however, may be half sibs. In order to assess
the potential effect of unknown half sib pairs in the data on the
analysis, the sensitivity of the ED sib pair statistic to a small fraction
of undetected half sib pairs was examined. We found that the undetected
half sibs increase false positive rate of linkage results. If the
investigator ascertains the half sib pairs, an appropriate test
incorporating them is derived.
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TITLE: Assessing the uncertainty in model selection --- the
confidence set of models.
SPEAKER: Hidetoshi Shimodaira
The Institute of Statistical Mathematics
Tokyo, Japan
DATE: December 6, 1999
LOCATION: Gov 104
TIME: 3:00 p.m.

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We consider multiple comparisons of log-likelihoods, or AIC values, to
take account of the multiplicity of testings in selection of nonnested
models. The result is obtained as a set of equally good models, which are
not significantly worse than the maximum likelihood model; i.e., a
confidence set of models. Our method is based on Shimodaira (1993, 1998).
When comparing just two models, this reduces to the test of Linhart
(1988), Kishino and Hasegawa (1989), and Vuong (1989); which is known as
K-H test, and is widely used in inferring the tree topology of molecular
phylogeny. K-H test can give overconfidence to a wrong tree topology (or
model in general), because the selection bias in the log-likelihood
difference is overlooked in it. Our method automatically corrects the
selection bias, and a numerical example of Shimodaira and Hasegawa (1999)
shows that some controversy over incompatible biological hypotheses of
phylogeny is due to the overconfidence. The uncertainty in topology
selection is partially due to the misspecification of the DNA substitution
process; we touch on a graphical diagnostic method for this problem. We
also discuss a connection between the method of "The Problem of Regions"
(Efron and Tibshirani, Annals of Statistics 1998) and our method of
multiple comparisons of log-likelihoods. The numerical examples include
mammalian phylogeny selection and the variable selection of regression
analysis.
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TITLE: GIS-based Approaches to Environmental Equity Assessment
SPEAKER: Thomas A. Louis
Division of Biostatistics
University of Minnesota
Visiting Scholar - Committee on National Statistics
National Academy of Sciences
DATE: December 16, 1999
LOCATION: Funger 320
TIME: 11:00

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EPA regulations require assessment of environmental equity (equitable
protection from the burdens of environmental hazards across sociodemographic
groups) in locating hazardous waste sites and in prioritizing environmental
remediation. Typical geographic assessments compare demographics of exposed
populations, while typical statistical assessments focus on differences in
health outcomes between demographic subgroups. Comprehensive assessments of
environmental equity link exposure, demographic and health information and a
Geographic Information System (GIS) enables an integrative approach.

I report on a general approach to quantifying exposure inequity based on
measuring differences between exposure distributions for subpopulations and
show how it can be used as a formal basis for site evaluation. Candidate
inequity metrics include distances between cumulative exposure distributions
and weighted distances with weights based on exposure-research relations.
Reported toxic emissions from Allegheny County, PA illustrate the approach.
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The contact person is Reza Modarres at Reza@gwu.edu

or 202-994-6359.