The following abstracts have been accepted and will be part of the
poster session at the Bayesian Workshop.
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by
Heidi W. Ashih and Giovanni Parmigiani
ISDS
Duke University
Box 90251
Durham, NC 27708-0251
heidi@stat.duke.edu
Abstract:
Two of the most common measures of disability/handicap used in stroke
are the Rankin Stroke Outcome Scale (R) and the Barthel ADL Index (B).
The Rankin Scale, which was designed for applications to stroke, is
based on assessing directly the global conditions of a patient. The
Barthel Index, which was designed for more general applications, is
based on a series of questions about the patient's ability to carry out
10 basic activities of daily living. The objective of our analysis is
to provide a method for translating between B and R, or, more
specifically, to estimate conditional probability distributions of each
given the other. Subjects consisted of 459 individuals who sustained a
stroke and who were recruited for the Kansas City Stroke Study, from
1995-1998. Patients were assessed with B and R measures 0,1,3 and 6
months after stroke. In addition, we incorporated a published 4x4 table
cross-classifying patients by aggregate Rankin and Barthel scores.
Our estimation approach is motivated by four goals: (a) overcoming the
difficulty presented by the fact that the two data sources report data
at different resolutions; (b) interpolating the empirical counts to
provide estimates of probabilities in regions of the table that are
sparsely populated; (c) avoiding estimates that would conflict with
medical knowledge about the relationship between the two tests and (d)
estimate the relationship between Ranking and Barthel scores at three
months after the stroke, while borrowing strength from measurements made
at zero, one and six months.
We handled (a) via data augmentation. We addressed both (b) and (c) via
an approach that recognizes the natural negative dependence in the
tables, and captures it without making any restrictive parametric
assumptions about the relationship among the cell probabilities. This
relationship is described via a condition that we termed local
association, which means that any two-by-two sub-table will show
association (in this case negative) among the scores. We addressed (d)
by postulating an autoregressive stochastic process for the cell
probabilities. Each cell probability table is modeled as a Dirichlet
distribution whose mean is given by the cell probability of the previous
time point. The Dirichlet distribution also includes a dispersion
parameter which, in our context, controls the average amount of
variation that occurs in the table from one time interval to the next.
Work carried out in collaboration with P Duncan, D Matchar, and G Samsa.
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by
Zeleke Worku
Technikon Natal
P.O. Box 953, Durban 4000, South Africa
zelekew@umfolozi.ntech.ac.za
and
Dan DeWaal
University of the Orange Free State
P.O. Box 339, Bloemfontein 9300, South Africa
Abstract:
Special regression models were constructed using
the Weibull and Cox models to explain the relationship between the
lifetime of under-five children and 9 explanatory variables, taking
the presence of censored observations and truncation at the age of
five years into account. The nine variables used for analysis were the
literacy status of the mother, the income status of the mother, the
place of delivery of the child, attendance of postnatal health care
services by the mother, availability of a nearby health facility, the
extent of malnutrition of the child, the presence of acute respiratory
infectious diseases, and the age of the mother at first birth. A
random sample of 4001 under-five children from the Maseru District of
Lesotho was used for data analysis. The normal distribution could not
be used to analyze the lifetime of childrren because the error terms
were not distributed normally with mean 0 and variance sigma
squared. As a result, the relationship between the lifetime of
children and the 9 variables listed above had to be analyzed using
Bayesian principles and Matlab programming, taking the presence of
censored obseravations and the need to truncate the age at 5 years. To
facilitate computation using Matlab for a PC, several subsamples of
size 400 were drawn from the sample for data analyais. Using Bayesian
inference, Weibull and Cox regression models were estimated. The
Weibull model fitted the data better than the Cox model.
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by
John B. Carlin
RCH Research Institute (University of Melbourne)
and University of South Florida
Epidemiology and Biostatistics, MDC-56
University of South Florida
Tampa, FL 33612
j.carlin@medicine.unimelb.edu.au
Abstract:
In an experiment on the effects of varying ventilation regimes on lung damage
in rabbits, six groups of between 6 and 8 animals each were compared, using
a factorial treatment structure of 3 frequency levels crossed with 2
amplitudes. The resulting data were reduced to binary outcomes for
each animal, producing a $3\times 2\times 2$ contingency table. Although
the numbers were small, there appeared to be a large effect of amplitude
at the two extreme frequency levels, but there were no failures
at either amplitude in the middle frequency group. The question of interest
was whether the data provided evidence that the effect of amplitude
differed between the 3 frequencies and in particular whether the effect in the
middle group was lower than in the two extreme groups. Various models were
considered for the 3 odds ratios in question, all seeking to incorporate
minimally informative prior assumptions. Because of the small numbers,
sensitivity to prior distribution specifications was considerable and in
particular we compared the effect of assuming independent prior distributions
on each cell in the $3\times 2$ factorial with that of using a more structured
prior distribution incorporating exchangeable row, column and interaction
effects. The analysis provides a case study of the sensitivity of inferences
in small samples, in a problem where the popular ``exact" frequentist
approach, based on a null hypothesis of equality of the odds ratios,
breaks down.
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by
Eiki Satake
Emerson College, School of Communication Sciences and Disorders
100 Beacon Street
Boston, MA 02116
esatake@emerson.edu@
Abstract:
In his seminal work on formal reasoning, Polya (1968) attempts to
establish a mathematical foundation for "plausible reasoning" based
on syllogistic structures that serve as heuristics for analyzing
patterns of reasoning, particularly inductive reasoning which he
sees as "conspicuous" in every day life. Polya argues that the
increment of the credibility of a conjecture always depends on the
strength of circumstantial evidence.
Kadesch's (1986) "new version" of Bayes' equation verifies the
conclusions of Polya"s syllogisms and heuristics but not in a
quantification of probabilities. The process described in this
paper demonstrates how Polya's syllogistic/heutistic approach to
plausible reasoning and Kadesch's "mathematical expressions" of
Polya's ideas may be quantified using Empirical Bayes'Estimation
through an example of criminal trial.
The use of Bayesian statistics appears both valid and preferable in
quantifying inductive reasoning patterns, such as those identified
by Polya. They allow probability statements to be made about the
plausibility of an event. Bayes' rule provides a methodology for
revising prior probabilities in light of additional evidence and is
eminently suitable in cases of circumstantial evidence.
In cases of a crimanal trial with a jury, the prosecutor and defence
attorney hold conflecting views and conjectures on the guilt or
innocence of the defendent. In each case, the views and conjectures
are subjective. The same is true of members of the jury. In a
trial by jury, the role of the jury is to determine whether the
evidence
submitted is of sufficient strength to convict or aquit.
In his discussion of judicial proof, Poyla suggests that the
reasoning by which a jury arrives at its decision follows an
inductive pattern analogous to scientific inquiry, where several
consequences of a conjecture are successively tested and evaluated .
In terms of patterns of plausible inference, continued verification
of a
conjecture renders the conclusion more credible.
Both Polya and Kadesch believe that the patterns of reasoning used
in these processes may be analyzed on logical and mathematical ways
to assess probabilityof a conjecture. In general, Polya uses
hypothetical syllogisms ("modus tollens") and heuristics, while
Kadesch employs a Bayesian analysis. However, in a discussion of
circumstantial evidence and reasoning in judicial matters, Polya
employs the "calculus of probability" in an attempt to learn the
credibility of evidence.
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by
Virdiana Lourdes, Mike West
ISDS
Duke University
Durham, NC
vl@stat.duke.edu
and
James Burgess
VA Management Sciences Group
Bedford, MA
Abstract:
As part of a long-term concern with measures of "quality-of-care"
in the VA hospital system, the VA Management Sciences Group is
involved in large-scale data collection and analysis of
patient-specific data in many care areas. Among many variable of
interest are observed times of "return to follow-up care" of
individuals discharged following initial treatment. Follow-up
protocols supposedly encourage regular and timely returns, and
observed patterns of variability in return time distributions are
of interest in connection with questions about influences on
return times that are specific to individual patients, care
areas, hospitals, and system-wide policy changes. The study
reported here takes a look at such issues in the area of
psychiatric and substance abuse patients across the nationwide
system of VA hospitals. The study is realtively new and ongoing,
and this paper presents the story of initial modelling and data
analysis efforts. We report on our studies of discrete duration
models that are designed to help us understand and estimate the
effects on return times that are specific to individual hospitals
-- the primary question for the VA -- in the context of a large
collection of potential additional covariates. We adopt logistic
regression models to describe discretised representations of the
underlying continuous return time distributions. These models
take into account categorical covariates related to the several
socio-demographic characteristics and aspects of medical history
of individual patients, and treat the primary covariate of
interest -- the VA hospital factor -- using a random
effects/hierarchical prior. Our model is analysed in parallel
across a range of chosen "return time cut-offs", providing a nice
analogue method of exploring and understanding how posterior
distributions for covariate effects and hyperparameters vary with
chosen cut-off. This perspective allows us to identify important
aspects of the non-proportional odds structure exhibited by this
very large and rich data set, by isolating important and
interesting interactions between cut-offs and specific
covariates. Summarisation of the sets of high-dimensional
posterior distributions arising in such an analysis is
challenging, and is most effectively done through sets of linked
graphs of posterior intervals for covariate effects and other
derived parameters. We explore and exemplify this work with a
full year's data, from 1997. The paper also discusses additional
questions of covariate selection via Bayesian model selection
methods, and other practical issues.
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by
D.J. De Waal
University of the Orange Free State
Department of Mathematical Statistics
P.O. Box 339, Bloemfontein 9300, RSA
wwdw@wwg3.uovs.ac.za
and
J. Beirlant
University of Kuleuven
Department of Applied Maths
Celestijnenlaan 200B
Heverlee 3001, Belgium
jan.beirlant@wis.kuleuven.ac.be
Abstract:
The data consists of the sizes (X) and the values (Y) of 1914
diamonds sampled from the Damaya and Bougban deposits in Guinea,
West Africa. The purpose is to model such multivariate data which
contain extreme values such as some large diamonds with high
values in order to construct similar data sets through simulations
and to estimate small tail area (volume) probabilities. Several
papers appeared in the literature on modelling bivariate extreme
values data with emphasis on peaks over threshold methods. The
model that we described here can be considered a general
multivariate parametric model with four types of parameters of
which one type contains the extreme value index. The MCMC
algorithm is used for estimating these parameters using the
maximal data information (mdi) prior. A simulation study on three
variables is also given together with model checking tools and an
illustration of extending the model to include covariates.
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by
Hikaru Hasegawa
Faculty of Economics and Business Administration
Hokkaido University
Kita 9 Nishi 7
Kita-ku, Sapporo 060--0809
Japan
hasegawa@econ.hokudai.ac.jp
Tran Van Hoa
Department of Economics
Wollengong
and
Rebecca Valenzuela
Melbourne Institute of Applied Economic and Social Research
University of Melbourne
Australia
Abstract:
The HOGLEX demand system (Tran Van
Hoa~\cite{TVH83,TVH85}) is integrable and completely general in the
sense that it encompasses all other well-known demand systems in the
literature on consumer behavior (Laitinen {\it et al.}~\cite{LTR83}).
The HOGLEX studies to date have been based on conventional OLS or MLE
methods and panel aggregate data. The paper elaborates on important
subsets of the HOGLEX demand system and, using household expenditure
unit records from two major ASEAN countries ({\it i.e.}, Thailand and
the Philippines), estimates by the Bayesian method these subsets for a
number of socio-demographic cohorts. We also estimate the models with
measurement error in total expenditure and compare the results with
those without measurement errors.
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by
Hedibert Freitas Lopes
DME, Universidade Federal do Rio de Janeiro and
ISDS, Duke University
Rio de Janeiro, Brazeil
hedibert@stat.duke.edu
Peter Muller
ISDS
Duke University
Durham, NC 27708
pm@stat.duke.edu
and
Gary Rosner
Duke University Medical Center
Durham, NC 27708
gary.rosner@duke.edu
Abstract:
We consider Bayesian meta-analysis to combine data from two studies
carried out by the Cancer and Leukemia
Group B (CALGB). Our analysis is based on a pharmacodynamic study
involving longitudinal data consisting of hematologic profiles, such
as blood counts measured over time, of cancer patients undergoing
chemotherapy. In both studies, we analyze the natural logarithm
of each patient's white blood cell count (WBC) over time
to characterize the toxic effects of treatment.
The WBC counts are modeled through nonlinear hierarchical
model that gather the information from both studies. Basically,
this is done by allowing the parameters defining the nonlinear
structure for each patient to depend on two mixture of
multivariate normals. The first mixture is shared common to both
studies, while the second mixture is study specific and captures
the variability intrinsic within patients from the same study.
The proposed methodology is broad enough to
embrace current hierarchical models and it allows for
{\em borrowing-strength} between studies in a new and simple way.
The development of MCMC techniques is flexible enough to allow
for posterior predictive inference of new patients and to account for
model uncertainty with respect to the number of components of the mixture,
for instance through a reversible jump algorithm.
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by
Daniela Golinelli and Peter Guttorp
Department of Statistics
University of Washington
Seattle, WA 98195
golinell@stat.washington.edu
Abstract:
Many processes in biology, ecology and physics are
modeled as continuous time stochastic processes. In the literature,
these models are rarely fit to data. This can partly be due to not
being able to observe such processes completely, so inference on the
parameters of interest becomes very involved. The reasons for
observing the population only partially may be due to efficiency or to
physical constraints, e.g. when the population of interest resides in
a living body. In such a context only samples or subsets of the
population may be observed at discrete times. This is the situation
that arises when studying hematopoiesis, the process of blood cell
production. The interest here is on having a better understanding of
hematopoietic stem cell (HSC) kinetics. HSCs are primitive blood cells
that support the entire blood and immune system.
We focus on the problem of making inference in hidden birth-death
processes, since a similar model, although somewhat more complicated,
has been used to model HSC behavior. The process is hidden because we
observe only a probabilistic function of the birth-death process
states at given observation times. We consider two cases. In the first
case, the hidden process is a one-dimensional birth-death process and
the observations are Poisson with rate given by a constant proportion
of the hidden population size. In the second, the hidden process is a
two-dimensional birth-death process, since, similarly to the HSC
example, we assume that half of the cells can be genetically marked
with a neutral marker. Hence, the observations are binomial, where the
probability of success is given by the proportion of the marked cells
in the hidden population at the observation times. In both cases, the
goal is to provide reasonable estimates of the birth and death rates.
A more classical approach to this inferential problem, that makes use
of the Forward-Backward algorithm, does not provide a satisfactory
solution. The two main reasons of its failure are: the infinite number
of possible hidden states, and the fact that the hidden process is
continuous in time while the observations are taken only at discrete
times. Using this approach involves the computation of transition
probability matrices of large dimensions. Since we do not know how
many states were visited by the hidden process during the observation
period, we are forced to put a bound on the size of the state
space. These transition probabilities are very unstable when the
observation times are far apart and computationally expensive.
However, a Bayesian approach, together with MCMC methods, seems to
overcome the problems stressed above and provide reasonable estimates
for the parameters of interest. Simulation results show that the true
parameter values fall in regions of high posterior probability. This
method shows great promise for solving an exciting problem in
hematology.
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by
Paola Sebastiani
Statistics Department
The Open University
p.sebastiani@open.ac.uk
Marco Ramoni
Knowledge Media Institute
The OpenUniversity
m.ramoni@open.ac.uk
and
Paul Cohen
Department of COmputer Science
University of Massachusetts
Amherst, MA
cohen@cs.umass.edu
Abstract:
The goal of this work is to enable mobile robots to learn the dynamics
of their activities. Our robot --- a Pioneer 1 --- is a small platform
with two drive wheels and a trailing caster, and a two degree of
freedom paddle gripper. For sensors, the Pioneer 1 has shaft encoders,
stall sensors, five forward pointing and two side pointing sonars,
bump sensors, a pair of infrared sensors at the front and back of its
gripper, and a simple vision system that reports the location and size
of color-coded objects. Our configuration of the Pioneer 1 has
roughly forty sensors, though the values returned by some are derived
from others. During its interaction with the world, the robot records
the values of about 40 sensors every 1/10 of a second. In an extended
period of wandering around the laboratory, the robot will engage in
several different activities --- moving toward an object, losing sight
of an object, bumping into something --- and these activities will
have different sensory signatures. It is important to the goals of our
project that the robot's learning should be {\em unsupervised}, which
means we do not tell the robot when it has switched from one activity
to another. Instead we define a simple event marker --- simultaneous
change in three sensors --- and we define an {\em episode} as the
period between event markers. The available data is then a set $S=\{
S_i \}$ of $m$ episodes for each sensor, and some episodes represent
the same dynamics. The statistical problem is to model the episodes
dynamics and then cluster the episodes that represent the same
dynamics to learn prototype experiences.
The solution we have developed is a Bayesian algorithm for clustering
by dynamics. We model the dynamic of each episode as a discrete Markov
chain (MC) and our algorithm learns MC representations of the
episodes dynamics and then clusters the episodes that give rise to
similar dynamics. The task of the clustering algorithm is two-fold:
find the set of clusters that gives the best partition according to
some measure, and assign each MC to one cluster. A partition is an
assignment of MCS to clusters such that each episode belongs to one
and only one cluster. The novelty of our approach is to regard the
task of clustering MCS as a Bayesian model selection problem. In
this framework, the model we are looking for is the most probable way
of partitioning MCS according to their similarity given the data. We
use the posterior probability of a partition as scoring metric to
assess its goodness of fit. As the number of possible partitions grows
exponentially with the number of MCS to be considered, we have a
heuristic method to restrict the search space. The algorithm performs
a bottom-up search by recursively merging the closest MCS
(representing either a cluster or a single episode) and evaluating
whether the resulting model is more probable than the model where
these MCS are separated. When this is the case, the procedure
replaces the two MCS with the cluster resulting from their merging
and tries to cluster two other MCS. Otherwise, the algorithm tries to
merge the second best, the third best, and so on, until the set of
pairs is empty and, in this case, returns the most probable partition
found so far.
This clustering method has allowed the robot to learn and discriminate
significant dynamics as passing an object on the left, or bumping into
an object.
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by
Piet Groenewald and Carin Viljoen
University of the Orange Free State
Department of Mathematical Statistics
P.O. Box 339, Bloemfontein 9300
RSA
wwpg@wwg3.uovs.ac.za
Abstract:
The data consists of the milk records of a number of Saanen dairy goat
herds, recorded over a period of two seasons. Farmers recorded, on
certain test days during the lacatation period, the milk production as
well as milk composition as to fat and protein content of each animal
in the herd. The data contains the records of 493 animals, 262 of
which were recorded for both seasons.
The purpose of the study is to determine the effect of certain
covariates on the characteristics of the lactation curve. The
covariates used are the season, the lactation number of the animal and
the time during the season at which lactation starts. Some of the
pertinent characteristics are the peak milk yield, time of peak milk
yield, total milk production and the relationship between milk
production and milk composition as well as between the lactation
curves of the same animal in successive seasons.
A hierarchical Bayes model is proposed, with Wood's model, a
three--parameter Gamma curve, as the observation model for milk
production as well as for the milk composition, normal/Wishart priors
for the observation model parameters and noninformative second--stage
priors.
By means of the Gibbs sampler, the posterior distributions of the
quantities of interest are obtained, and they clearly illustrate the
significant effect of some of the covariates on the characteristics of
the lactation curve. The analysis also enable us to estimate the
lactation characteristics of untested animals, predict future
characteristics and identify exceptional animals.
This is an ongoing project, and a number of issues, important to dairy
goat breeders, still need to be examined.
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by
Lurdes Y.T. Inoue, Peter Muller, Gary Rosner and Mark Dewhirst
Duke University
P.O. Box 90251
Durham, NC
lurdes@stat.duke.edu, pm@stat.duke.edu,
grosner@cstatz.mc.duke.edu, dewhirst@radonc.duke.edu
Abstract:
This research is motivated
by experiments evaluating the hemodynamic effects of various agents in
tumor-bearing rats. In one set of experiments, the mice breathed room
air, followed by carbogen (a mixture of pure oxygen and carbon dioxide).
Interest focuses on answering the questions:
Do individual profiles change once the breathing mixture changes?
How does the location of the tumor alter the effect of carbogen on
hemodynamics? Do tumors respond to carbogen differently than normal
muscle tissue?
We propose a model for longitudinal data with random effects which
includes model based smoothing of repeated measurements over time,
implemented with a flexible state space model.
Submodels for repeated measurements on different individuals are
hierarchically linked to allow borrowing strength across the
population and formal inference about the effects of
individual-specific covariates.
The model is appropriate for the analysis of repeated measurement data
when no convenient parametrization of the longitudinal data is
suggested by the underlying application or exploratory data analysis,
and the only available information is related to smoothness of
measurements over time.
The experimental responses are longitudinal measurements of oxygen
pressure measured in tissue, heart rate, tumor blood flow, and mean
arterial pressure. The nature of the recorded responses does not
allow any meaningful parametric form for a regression of these profiles
on time. Additionally, response patterns differ widely across individuals.
Therefore, we propose a non-parametric regression to model the profile
data over time.
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by
Dalene Stangl, Lurdes Inoue and Steve Ponisciak
ISDS, Duke University
Box 90251
Durham, NC 27708-0251
dalene@stat.cmu.edu
Abstract:
Many meta-analyses in clinical trials and health policy examine
time-to-event outcomes. However, these studies often rely on
published summary data that presents the outcome as a discrete
variable observed at a single point in time. In other studies the
continuous time-to-event outcome is modeled, but controversy over the
use of fixed versus random-effect parametric and semiparametric models
ensues. This paper examines the trade-offs between these modeling
choices.
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by
Paola Sebastiani
The Open University
p.sebastiani@open.ac.uk@
Marco Ramoni and Alexander Crea
Knowledge Media Institute
The Open University
m.ramoni@open.ac.uk, a.crea@open.ac.uk
Abstract:
A typical problem of mailing campaigns is the low response rate. Recent
studies have shown
that adding incentives or gifts in the mailing can increase the response
rate. This is the strategy
implemented by the Paralyzed Veterans of America (PVA) in the June '97
renewal campaign. The
mailing included a gift of personalized name and address labels plus an
assortment of 10 note cards
and envelopes. Each mail cost the charity 0.68 dollars and resulted in a
response rate of about
5\%. Since the donations received by the respondents ranged between 2
and 200 dollars, and the
median donation was 13 dollars, it is important to decide when and why
it is worth pursuing the
campaign, on the basis of the information available from in-house data.
Last year, PVA made available a database of about 100,000 cases and
470 variables for the so
called {\sf KDD Cup}: a contest in which both commercial and research
prototypes for Knowledge
Discovery in databases ({\sf KDD}) were invited to build a model
maximizing the profit from the
renewal mailing. The database consists of variables measuring directly
donors features (as donors
history, age, income etc) and variables collected from the 1990 US
Census to characterize the
donors neighborhood as well as socio, economic, urbanicity and ethnicity
indicators. The winner
was the company GainSmart that modeled independently the probability of
response via logistic
regression and the donation amount via multiple linear regression. The
two models can be used
jointly to decide when it is worth pursuing the mailing, by evaluating
the expected profit.
However, the two models do not provide much insight about the
relationships between the variables
that appear to affect mostly both response rate and donation amount. For
example, one may be
interested in profiling the donor to be targeted in the next campaigns
or try to understand the
donor behavior. This is the objective of our work.
By extending the approach of winner GainSmart, we build three dependency
models. The first one
({\sf Response-net}) models the dependence of the probability of
response to the mailing campaign
on the independent variables in the database removed of the variables
collected from the 1990 US
Census. The second one ({\sf Donation-net}) models the dependence of the
donation amount and it is
built by using only the 5\% respondents to the mailing campaign. The
third model is a Naive Bayes
classifier that models one global indicator of the socio-economic
status, the urbanicity, ethnicity
and a variety of other demographic characteristics as summary of the
variables collected from the
1990 US Census. The three models are Bayesian Networks %\cite{Pearl88}
(Pearl, 1988)
induced from data using {\sf
Bayesware Discoverer} a commercial product for the induction of Bayesian
Networks from possibly
incomplete data produced by {\sf Bayesware Ltd}. \bkd\ induces Bayesian
Networks from data using
Bayesian methods, as described for example in
%\cite{Ramoni.Idabook99},
Ramoni and Sebastiani (1999)
and implements the {\em
Bound} and {\em Collapse} method of %\cite{Ramoni.JIDA98}
Ramoni and Sebastiani (1998) to compute a
first order approximation of
the scoring metric when data are incomplete %\cite{Ramoni.UAI97}.
(Ramoni and Sebastiani (1997).
Bayesian networks provide a compact and easy-to-use representation of
the probabilistic information
conveyed by the data. The network structure aids one to understand the
dependencies among the
variables. However, the network structure is only one aspect of the
knowledge represented. By
quering the network, one can investigate different relationships between
the variables, as well as
making prediction and explanation. For example, the BBN {\sf
Response-net} shows that the
probability of a donation is directly affected only by the wealth rating
and the number of lifetime
gifts to card promotions prior the mailing campaign. Whether a donor
responds is independent of all
the variables in the net given the wealth rating and the number of
lifetime gifts, so that these
variables are sufficient to predict the donors response. However, by
querying the network, we can
profile respondents who, for example, appear to be are most likely elder
females, with an average
household income, who live in an area with a percentage of Vietnam
veterans between 25 and 50. The
BBN {\sf Donation-net} shows that the donation amount is directly
affected by the last gift prior
the mailing campaign and the number of times the donor responded to
mail order offers from news
and financial publications. Apparently, donors tend to maintain the gift
amount constant and their
constancy is directly proportional to the number of times they responded
to similar mail offers.
The last model --- the Naive Bayes classifier --- is an ancillary model
to show the predictive
capability of one global indicator as a classification of the variables
collected from the 1990 US
census. The large predictive capability of this indicator sustains the
decision to remove the US
census variables from the database.
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by
Richard Evans
University of Arkansas
4301 W. Markham Street
Slot 781
Little Rock AR 72205
evansrichadb@exchange.uams.edu
Siu Hui
Indiana University
and
Joe Sedransk
Case Western Reserve University
Abstract:
Bone mineral density (BMD) at the spine and at the hip is
central to the managment of osteoporosis because fractures at the
spine are the most prevalent while fractures at the hip are the
most debilitating. It has been shown that BMD predicts fractures
and that the rate of bone growth and loss with age are important
determinants of osteoporosis in old age. In order to develop therapies
for osteoporosis we need to understand the pattern of bone growth
and loss as people age. The problem is to estimate the ages cooresponding to the changepoints demarking the stages in the pattern of age specific mean rates of change of BMD, $\mu(t)$, $t=8,
\dots , 80$ where $t$ is age in years.
In this paper we assume the condition that the $\mu(t)$ behave
according to
$\mu(8)<\dots<\mu(t_1)>\dots>\mu(t_2)=0>\dots>\mu(t_3)<\dots<\mu(80)$,
and provide inference for the changepoints $t_1$, $t_3$, and $t_3$.
The constrained parameter Gibbs sampler suggested by
Gelfand, Smith, and Lee (1992) will not work for this problem
because $t_1$, $t_3$, and $t_3$ are uniquely determined conditional
on $\mu(t)$, and the order restriction of $\mu(t)$ is determined
conditional on $t_1$, $t_3$, and $t_3$. Instead, we use the Metropolis
Algorithm. Sampling the order restricted $\mu(t)$ is facilitated
by transforming the $\mu(t)$ to $z(t)$, where the $z(t)$ do not
have an order restriction. For example
$\mu(t)=\sum_{j=1}^{t}e^{z(j)}$, $t
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by
Chin-pei Tsai and Kathry Chaloner
School of Statistics
University of Minnesota
352 Classroom Office Building
199 Buford Ave.
St. Paul MN 55108
cptsai@stat.umn.edu, kathryn@stat.umn.edu
Abstract:
Two examples of large clinical trials for the treatment
of advanced HIV disease are described. For the two trials Chaloner
and Rhame (in ``Ethical and Statistical Reasons for Quantifying
and Documenting Prior Opinions'' manuscript (1999))
elicited prior opinions from over 50 HIV
clinicians. Their prior opionions are used here for design: the
sample size for reaching consensus with high probability is
calculated. Consensus is said to occur when all clinicians have
posterior opinions which would lead to prescribing the same
treatment. Posterior beliefs are calculated using a simple linear
Bayes approximation. In addition plots are given for determining
parameter values for which a particular sample size is sufficient
for consensus to be reached with high probability. These
calculations are useful tools at the design stage and are easy to
implement.
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by
J. Alex Stark, Kay Tatsuoka
National Institute of Statistical Sciences
Research Triangle Park, NC
stark@niss.org
and
Francoise Seillier-Moiseiwitsch
Department of Biostatistics
UNC Chapel Hill
Chapel Hill, NC
Abstract:
Reconstructing phylogenies (evolutionary histories) of proteins from
a set of observed sequences is an important statistical modelling
task in molecular evolution. Maximum likelihood and Bayesian
methods have been used for phylogenetic inference. We review Markov
chain Monte Carlo schemes that have been developed, and discuss the
application of these to HIV data. We consider the problem of
analysing the results from one such sampler and describe in detail a
method for determining a consensus labelled history. This is
illustrated with an example of HIV protease.
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by
J. Lynn Palmer and Mark Munsell
UT M.D. Anderson Cancer Center
Departmentof Biostatistics
Houston, TX 77030
jlp@odin.mdacc.tmc.edu
Abstract:
In cancer clinical trials, the usual Phase I methodology used to
determine appropriate dosages for Phase II studies is some variant
of the usual 3+3 design. In this method 3 patients are
entered at a specific dose level then 3 more at a higher dose
level until 1 or more patients experience toxicity. This method
usually selects as a Maximum Tolerated Dose (MTD) a dose level that
results in 25% to 33% of patients experiencing toxicity. However, in
some situations, a higher 'optimal' level of toxicity must be found,
as in when the toxicity is considered mild or fully reversible, or in
the situation when no toxicity arises the patient may be at a
higher risk. The latter situation occurred in a bone marrow
transplant application where the major toxicity was graft-versus-host
disease and a higher than standard toxicity rate was necessary.
Two methodologies are considered and compared through the use of
simulated data: the Continual Reassessment Method (CRM) and a
variation of the standard 3+3 methodology which also includes 12
patients treated at the MTD for somewhat higher precision. The two
methods alternated between being defined as the 'best' method to use
when this definition was based on expected toxicity levels at given
doses.
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by
Herbert Lee, Dave Higdon, Marco Ferreira and Mike West
Duke University
ISDS, Box 90251
Durham, NC
herbie@stat.duke.edu, higdon@stat.duke.edu, marco@stat.duke.edu, mw@stat.duke.edu
Abstract:
Conventional deterministic simulation models of fluid flow in porous
media require very high-dimensional parameters as inputs -- these
parameters are permeability and porosity tensor fields. Variations in
such parameters impact on multiple scales since fine-scale variations
in their values can have key large-scale effects on fluid flow
predictions. Critical interests lie in modeling and accounting for
uncertainty about such high-dimensional parameters, and in studying
the effects of such uncertainties on deterministic simulations of
fluid flow as an aid to practical problems such as contaminant
clean-up and oil reservoir exploration. Unfortunately, the
determination of these parameters is radically ill-posed, relevant
"hard" data is often limited and use must be made of various sources
of indirect data and expert opinion. In connection with a large
collaborative project involving statisticians, mathematicians,
computer scientists and engineers, we are developing high-dimensional,
multi-scale Markov random fields as prior models for permeability and
other parameters. Novel multi-scale modeling ideas attempt to account
for relationships between permeabilities on discrete grids at
different levels of physical resolution. This structure also allows
computations to be handled by a parallel computing machine, increasing
the size of problems that can be feasibly tackled, and also, at least
in prospect, introducing novel dimensions to the statistical thinking
about just what can and cannot be done in challenging, large-scale
problems.
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by
Peter Hoff, Michael Newton and Richard Halbert
University of Wisconsin, Madison
Department of Statistics
1210 W. Dayton
Madison, WI 53706-1685
hoff@stat.wisc.edu
Abstract:
People with familial adenomatous polyposis (FAP)
develop hundreds of tumors of the colon which, if left untreated,
eventually progress to become carcinomas. The disease is caused by the
inheritance of a single mutant allele of the \emph{APC} gene.
The \emph{Min} mutation in the mouse homologue of \emph{APC}
causes a phenotype very similar to human FAP. Mice with the \emph{Min}
mutation thus provide a model for studying this type of inherited
colon cancer.
In a mutagenesis experiment, a mouse is obtained which shows signs
of carrying a mutation reducing the tumor-causing effects of
\emph{Min}. In order to map the location of this modifier gene, it
is necessary to breed and identify a group of animals carrying
the modifier. Although inheritance of the modifier is not
directly observable, animals resulting from a breeding
experiment carry the modifier with known prior probabilities.
Conditional upon the unobserved pattern of inheritance, the animals
are modeled as having tumor counts distributed according to either a
carrier or a non-carrier distribution. Our goal is to identify likely
carriers and non-carriers of the modifier, assuming only
that the tumor count distributions are stochastically ordered. We
take a nonparametric Bayesian approach by putting a prior on the
space of pairs of stochastically ordered distributions, and develop
a Markov Chain for estimating posterior quantities of interest.
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Bayesian Hot Spot Detection in the
Presence of a Spatial Trend: Application to Total Nitrogen Concentration in the Chesapeake Bay
by
Victor De Oliveira
Departmento de Computo Cientifico y Estadistica
Universidad Simon Bolivar
Caracas, Venezuela
vdo@cesma.usb.ve
and
Mark D. Ecker
Department of Mathematics
University of Northern Iowa
Cedar Falls, IA
ecker@math.uni.edu
Abstract:
In the Chesapeake Bay, a decreasing gradient of
total nitrogen concentration extends from the
highest values in the north at the mouth of the
Susquehanna River to the lowest values in the south near the Atlantic Ocean. We propose an attractive model for these data with right skewed
sampling distributions by coupling the Box-Cox family of power transformations with a spatial trend in a random field model. This is done by
using a Bayesian Tranformed Gaussian random field, as proposed by De Oliveira, Kedem and Short 1997),
where we extend this model to the case when data
contain measurement error and propose a new Monte
Carlo algorithm to perform the necessary inference
and prediction. Also, we propose a new definition
of `hot spot' that generalizes previous definitions and is appealling for processes with a spatila trend.
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by
Soledad A. Fernandez, Rohan L. Fernando and Alicia L. Cariquiry
Statistics Department
Iowa State University
202C Snedecor Hall
Ames, IA 50014
soledad@iastate.edu
Abstract:
Markov chain Monte Carlo (MCMC) methods have been recently proposed
to overcome computational problems in linkage analysis. This
approach consists in sampling genotypes at the marker and trait
loci. It has been shown that the Markov chain that corresponds to
the scalar Gibbs sampler may not be irreducible when the marker
locus has more than two alleles. This problem does not arise if the
marker genotypes are sampled jointly from the entire pedigree. When
the pedigree does not have loops, a joint sample of the marker
genotypes can be obtained efficiently by using a modification of the
Elston-Stewart algorithm. When the pedigree has many loops,
obtaining a joint sample may be very time consuming. We propose a
method for this situation, in which we sample genotypes from a
pedigree so modified as to make joint sampling efficient. These
samples, obtained from the modified pedigree, are used as candidate
draws to be accepted or rejected in the Metropolis-Hastings
algorithm. The efficiency of this strategy is compared to the
efficiency of other approaches in the literature.
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by
Vanja Dukic
Division of Applied Mathematics
vanja@stat.brown.edu
and
Joseph Hogan
Center for Statistical Sciences
Brown University
Providence, RI 02912
Abstract:
In Vitro Fertilization and Embryo Transfer (IVF-ET) is considered
a method of last resort for treating infertility. Oocytes taken
from a woman are fertilized in vitro, and one or more resulting
embryos are transferred into the uterus. An important outcome of
interest in IVF studies is embryo implantation. A widely used
model, known as the EU model, postulates that implantation
probability is explained by a combination of embryo viability (E)
and uterine receptivity (U). Specifically, the model assumes that
uterine receptivity is characterized by a latent binary variable
U, and that the number of viable embryos among those selected for
transfer, E, is binomial. The observed number of
implantations among the transferred embryos is the product of E
and U.
The case study concerns estimating the effect of hydrosalpinx on
embryo implantation in patients undergoing IVF. Hydrosalpinx is
a build-up of an embryotoxic fluid in the
fallopian tubes, which sometimes leaks to the uterus and may
reduce the likelihood of implantation. It is generally
understood that hydrosalpinx does not affect embryo viability,
which is determined prior to transfer; rather, it affects
implantation rate by compromising the uterine environment.
Affected tubes can be treated surgically, but the procedure may
result in permanent damage to the tubes and loss of their
functionality. Among IVF practitioners and researchers, there
exists considerable disagreement about whether hydrosalpinx
reduces implantation rates enough to warrant surgery as a general
treatment. Perhaps owing to high risk associated with surgery,
very little data from clinical trials is available; many of the
arguments for and against the use of surgery rest on findings
from observational studies. Few of these studies are analyzed
using methods for correlated data, and many do not even employ
covariate adjustment.
Our case study is based on data from an observational study of
288 women undergoing IVF because of tubal disease. We use our
hierarchical version of the EU model to assess the effect of
hydrosalpinx on implantation by estimating its effect on uterine
receptivity. When some subjects have zero implantations, the EU
model is not fully identified and informative prior distributions
are required for key parameters. Our analysis uses informative
priors constructed from previous studies, and examines
sensitivity to choice of prior distribution. The analysis also
indicates substantial subject-level heterogeneity with respect to
embryo viability, suggesting the importance of using a
multi-level model.
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by
Robin Fisher and Jana Asher
HHES Division, 1065-3
U.S. Census Bureau
Washington, DC 20233-8500
jana.l.asher@ccmail.census.gov
Abstract:
The U.S. Census Bureau Small Area Income and Poverty
Estimates program produces biennual intercensal
estimates of the povery rates and counts of poor within counties for
use in determining the allocation of federal funds to local
jurisdictions. Our main consumer is the Department of Education,
which indirectly uses these estimates to distribute approximately \$7
billion of Title I funds annually. Numbers of poor are
currently modelled through an empirical Bayes estimation method
centered on a linear regression; the dependent variable
is a log transformation of the three-year
average of the March Current Population Survey (CPS) estimate of the number
of poor for each county, and the independent variables are log transformations
of administrative data such as the number of poor from the previous decennial
census, the number of poor as aggregated from tax return data, and the food
stamp participation rate for each county.
We assume the variability of the CPS estimates is the sum of a model error term
with constant variance, and a sampling error term whose variance is
proportional to the inverse of a power of the CPS sample size. Maximum
likelihood estimation is used to jointly determine the values of the
regression coefficents and the sampling variance components. Problems
with the current estimation technique include a loss of data points due
to the log transformation for
counties whose CPS sample of poor is zero,
and the requirement of
using decennial census data to estimate the model error variance term.\\
To eliminate these problems and improve the overall quality of our estimates,
we have developed a hierarchical
Bayesian model which assumes the observed number of poor is a scaled
binomial random variable given the underlying poverty rate. This
poverty rate, in turn, has a beta prior which relies on a set of parameters
that includes the regression coefficents for the administrative data.
Posterior probability distributions for regression parameters, variance
parameters, and true proportion poor are generated using Markov Chain Monte
Carlo techniques. We will discuss the Bayesian model and compare the results
of the original and new estimation methods.
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by
David A. van Dyk
Department of Statistics
Harvard University
vandyk@stat.harvard.edu
Vinay L. Kashyap and Aneta Siemiginowka
Harvard-Smithsonian Center for Astrophysics
and
Alanna Connors
Department of Astronomy
Wellesly College
Abstract:
In this paper, we employ
modern Bayesian computational techniques (e.g., EM-type algorithms,
the Gibbs sampler, and Metropolis-Hastings) to fit new models for low-count,
high-resolution astrophysical spectral data. Our
methods will be useful not
only for the Chandra X-ray Observatory (launched
by the Space Shuttle {\it Columbia}, July, 1999), but also for
such new generation telescopes as XMM, Constellation-X and GLAST.
This application demonstrates the flexibility and power of modern
Bayesian methodology and algorithms to handle highly hierarchical
models that account for the complex structure in the collection of
high-quality spectra.
Current popular statistical analysis for such data typically involves
Gaussian approximations (e.g., chi squared fitting) which are not
justifiable for the high-resolution low-count data that will soon be
available. In contrast,
we explicitly model photon arrivals as a Poisson process and,
thus, have no difficulty with high resolution data
Our models also incorporate instrument response (e.g. via
a response matrix and effective area vector) and background
contamination of the data. In particular,
we model the background as the realization of a second
Poisson process, thereby eliminating the need to directly
subtract off the background counts and the rather
embarrassing problem of negative photon counts. The source
energy spectrum is modeled as a mixture of a generalized
linear model which accounts for the spectral continuum plus
absorption (i.e,. stochastic partial censoring) and several
(Gaussian) line profiles.
Using several examples, we illustrate how Bayesian
posterior methods can be used to compute point
estimates of the various model parameters as well
as compute error bars on these estimates.
.
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by
M.J. Bayarri
University of Valencia
Av. Dr. Moliner 50
Burjassot, Spain
susie.bayarri@uv.es
and
A.M. Mayoral
Miguel Hernandez University
Av. Ferrocarril s/n
03202 Elche
Spain
asun.mayoral@umh.es
Abstract:
The degenerating effect of schizophrenia in the brain is an issue
attracting considerable interest in the psychiatric literature. In
particular, several experiments studying the possible changes
in brain morphology of schizophrenics have been reported. The quality,
measurement
techniques, diagnostic tools and measure of brain 'size'
considered were widely different among those experiments.
Seven of them investigating the change in the Ventricular Brain
Ratio (VBR) of schizophrenics and for which complete data existed,
were retrieved from
the literature . While some of them defended the
theory that VBR tends to shrink in schizophrenics, some others
defended precisely the opposite. In this paper, a Bayesian
meta-analysis of these seven experiments is performed and
inferences about the VBR change per year addressed . Possible
biases due to diagnosis procedure and diagnosis criteria are taken
into account.
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by
Scott C. Schmidler, Jun S. Liu and Douglas L. Brutlag
Section on Medical Informatics
and Dept. of Statistics and Biochemistry
Stanford University
Medical School Office Bldg, X215
Stanford, CA 94305
schmidler@smi.stanford.edu
Abstract:
The Human Genome Project estimates that sequencing of the entire
complement of human DNA will be completed in the year 2003. At the same
time a number of complete genomes for pathogenic organisms are already
available, with many more under way. Widespread access to this data
promises to revolutionize areas of biology and medicine, by providing
fundamental insights into the molecular mechanisms of disease and
pointing the way to the development of novel therapeutic agents. Before
this promise can be fulfilled however, a number of significant hurdles
remain. Each individual gene must be located within the 3 billion bases
of the human genome, and the functional role of its associated protein
product identified. This process of characterization of function, as
well as later development of pharmaceutical agents to affect that
function, is aided greatly by knowledge of the 3-dimensional structure
into which the protein folds. While the sequence of the protein can be
determined directly from the DNA of the gene which encodes it,
prediction of the 3-dimensional structure of the protein from that
sequence remains one of the great open problems of science. Moreover,
the scale of the problem (the human genome is projected to contain
approximately 100,000 genes) necessitates the development of
{\em computational} solutions which capitalize on the laboriously
acquired experimental structure data.
We describe our work on Bayesian models for prediction of protein
structure from sequence, based on analysis of a database of experimentally
determined protein structures. We focus on a well-known simplification of
the problem which attempts to predict the "secondary structure" of
the protein, by identifying regions in a protein sequence which take
on regular local conformations in the (unobserved) 3-dimensional structure.
We define joint probability models for sequence and structure which capture
fundamental aspects of the folding process such as hydrophobicity patterns
and side chain interactions. A simple model assuming conditional
independence of local "segments" is developed which allows efficient
calculation of predictive quantities using dynamic programming
algorithms based on graphical Markov models. This approach is shown
to perform at the level of the best available methods in the field
via extensive cross-validation experiments. We then show how the
model is naturally extended to include non-local sequence interactions
arising from 3-dimensional folding of the protein. With the use of MCMC
simulation techniques, such extended models may allow us to go beyond the
realm of secondary structure prediction to the location of contacts in
the folded 3-d structure, hence narrowing the gap between sequence and
completely folded structure.
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by
Sudip Bose
Dept. of Statistics
The George Washington University
2201 G. Street, NW
Washington, DC 20052
sudip@gw.edu
Abstract:
We carry out a Bayesian analysis of the performance of a stock selection method
based on selecting high-yielding stocks from the Dow Jones Industrial Index
(the Dow 30). In particular we compare its return to that of the Dow Jones
Index itself. Ever since John O'Higgins book "Beating the Dow" which described
three simple, related strategies based on Dow Jones stocks that combined high
yield with low price, there has been much interest in such strategies, and
mutual-fund families have even formed investment trusts for the general public
based on such methods. We examine whether a particular such strategy does
indeed outperform the Dow, and check for robustness of our conclusions.
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by
Lynn E. Eberly and Bradley P. Carlin
Division of Biostatistics
School of Public Health
University of Minnesota
420 Delaware St. SE, Box 303
Minneapolis, MN 55455
lynn@biostat.umn.edu
Abstract:
In this paper we analyze a dataset of county-level lung cancer rates
in the state of Ohio during the period 1968--1988, and their possible
relation to a nuclear fuel reprocessing plant near the Cincinnati
metro area. In order to answer important related questions in
environmental justice, complex spatio-temporal models are required.
Here, separate random effects for capturing unstructured heterogeneity
and spatial clustering are of substantive interest, even though only
their sum is well-identified by the data. Often the quantity of
interest is the posterior empirical proportion of variability due to
each effect. Because of its empirical nature, it is not immediately
clear from what sort of prior this quantity is derived. We
investigate whether or not our data can even inform about this
quantity, i.e., if there is Bayesian learning occurring. We conclude
Bayesian learning is possible in these settings, and discuss the
impact of this result on our particular example, as well as on the
practice of Bayesian spatial data analysis more generally.
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by
Dave Higdon and Richard E. Miller
Institute of Statistics and Decision Sciences
and Zoology
Duke University
Box 90251
Durham, NC 27708-0251
higdon@stat.duke.edu
Abstract:
Selection can be defined as the covariance between
relative fitness and traits within a population of
individuals. However, this covariance is often greatly
influenced by the dependence of the focal traits
and fitness on the local environment. An alternative
approach recently developed by Rausher
has shown that a genetical analysis corrects for this
potential confounding influence of local environment.
Traditional application of this method has been to
first estimate breeding values for both the traits
and fitness using family means and then use these
values in the selection analysis. Here we present an
alternative statistical approach developing a Bayesian
hierarchical model for the genetical analysis of selection.
We consider a case study that investigates
the pattern of selection across four
environments in a population of the common morning glory,
Ipomoea purpurea. The focal trait here is plant size
measured as leaf area late in the growing season. Fitness
is estimated both as seed number (female component of
fitness) and flower number (male component of fitness). The four
environments are competition treatments implemented to create
a gradient from high to low competition. The plants
used in this experiment come from a half-sib breeding design
producing progeny of known parentage. The large number of
individuals used in this experiments ($N = 3,240$)
requires a large planting area, therefore sources of
unmeasured environmental variation need to be accounted for
when estimating the breeding values for the traits and fitness.
Our Bayesian hierarchical model comes in two stages:
\begin{itemize}
\item
a model for the data to estimate breeding values for
plant size and fitness;
\item
a model for the
relationship between plant size and fitness estimated as
breeding values.
\end{itemize}
Such models have previously been tackled in two separate estimation
steps: obtraining family estimates for fitness and the traits;
and examining the relationship between size and
fitness using standard regression techniques involving these
estimates. This may not properly account for structure as well
as uncertainty in the problem. Our Bayesian hierarchical modeling
approach handles both stages of this model simultaneously,
allowing information, structure, and uncertainty to propagate
between its various stages. In addition to its hierarchical
structure, this model features a
bivariate spatial model to more realistically account for
environmental covariation in plant size and fitness.
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by
Fabrizio Ruggeri and Antonio Pievatolo
CNR-AIMI
Via Ampere 56
20131 Milano, Italy
fabrizio@iami.mi.cnr.it
Abstract:
We present some findings from a consulting job on gas escapes in an
urban gas distribution network. Poisson processes are used to describe
the escapes in both iron cast (homogeneous process) and steel
pipelines (nonhomogeneous process). Particular attention is devoted to
the elicitation of the experts' opinions. Both design and maintenance
of the network are considered, focussing on the effects of some
quantities like different sources of corrosion and location.
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by
Steven N. MacEachern and Mario Peruggia
The Ohio State University
Department of Statistics
Columbus, OH 43210
peruggia@stat.ohio-state.edu
Abstract:
We consider a strategy for Bayesian model building that begins by
fitting a simple, default model to the data.
Numerical and graphical
exploratory tools, based on
summary quantities from the default
fit, are used to assess the adequacy of the initial model
and to identify directions in which the fit can be refined.
We apply this strategy to build a Bayesian regression model
for a classic set of data on brain and body weights of mammalian
species. We discover inadequacies in the traditional regression model
through use of our exploratory tools.
More sophisticated models point the way toward judging the
adequacy of a theory on the relationship between body weight and brain
weight, and also bear on the
timeless question ``Do we have big brains?''
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by
Cavan Reilly and Andrew Gelman
Department of Statistics, Columbia University
618 Mathematics NY,Ny 10027
cavan@stat.columbia.edu
Abstract:
We develop a new method for the construction of
more precise estimates of a collection of population means using
information about a related variable in the context of repeated sample
surveys, and we illustrate this method using presidential approval
data (our related variable is political party identification). We use
post-stratification to construct these improved estimates, but since
we don't have population level information on the post-stratifying
variable, we construct a model for the manner in which the
post-stratifier develops over time. In this manner, we obtain more
precise estimates without making possibly untenable assumptions about
the dynamics of our variable of interest, the presidential approval
rating.
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by
Sandip Sinharay and Hal Stern
Iowa State University
Department of Statistics
Ames IA 50011
ssray@iastate.edu
Abstract:
A generalized linear mixed model is applied to data from a natural
selection study where the probability of an animal's survival is
modeled as a
function of family (random effect) and physical characteristics (fixed
effects). In this application, the magnitude of the variance component
corresponding to the random effect is of scientific interest as are
the fixed effects. A number of approaches are reviewed for
approximating the Bayes factor comparing the model with and without
random effects. We also use simulated data to assess the performance of
the different approaches.
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Role of Context in Visual Perception: A
Functional Magnetic Resonance Imaging Study
by
Thomas Nichols, Bill Eddy, Jay McClelland and Chris Genovese
Department of Statistics and
Center for Neural Basis of Cognition
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
nicholst@stat.cmu.edu, bill@stat.cmu.edu,jlm@cnbc.cmu.edu,genovese@stat.cmu.edu
Abstract:
We used Functional Magnetic Resonance Imaging (fMRI) to investigate
competing models of visual perception. One model, the ``bottom up''
model, predicts that context plays a post-perceptual role, outside the
primary visual cortex (V1). The other model, the interactive
activation model, predicts that context actually alters perception, a
process that occurs in V1. We use an intriguing perceptual effect to
look for context-dependent changes in V1.
Working closely with a cognitive psychologist, we developed ambiguous
visual stimuli (words flashed for 14 ms) that could be selectively
disambiguated by context (sentences missing an obvious last word).
Working with MR physicists we created custom stimuli presentation
software and hardware and determined MR acquisition parameters
appropriate for high temporal resolution imaging of V1. We used
comprehensive modeling for both preprocessing and inference: For
preprocessing we used the methods implemented in FIASCO (Functional
Imaging Analysis Software---Computational Oleo) to remove
systematic variation due to both the imaging hardware and the subject;
for inference we used both basic classical inference tools and the
Bayesian models available in BRAIN (Bayesian Response Analysis and
Inference for Neuroimaging). The modeling framework in BRAIN,
presented in the 4th Case Studies in Bayesian Statistics Workshop, was
originally intended for block-design fMRI (where stimuli are presented
over 30 second to 2 minute intervals) but we show that it can be
applied to the new event-related fMRI (where transient stimuli are
used). We also demonstrate how the multiple comparison problem can be
ameliorated by using functionally-defined masks, which constrain
the analysis to a small anatomical region.
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by
Pam Abbitt
North Carolina State University
CAMPUS BOX 8203
RALEIGH, NC 27695
abbitt@stat.ncsu.edu
Abstract:
{The MLRA (Major Land Resource Area) 107 pilot project involved
implementation of a multi-phase probability sampling design for
updating the soil surveys for two counties in western Iowa. Many of
the data collection items in the survey are recorded for each
horizon (or layer) of soil. We consider estimation of quantiles for
soil texture profiles using a hierarchical model and data from the
pilot project. Soil horizon profiles are modeled as realizations of
Markov chains. Conditional on the horizon profile, transformed
field and laboratory determinations of soil texture are modeled as
multivariate normal. The posterior distribution of unknown model
parameters is numerically approximated using a Gibbs sampler. The
hierarchical model provides a comprehensive framework which may be
useful for analyzing many other variables of interest in the pilot
project.}
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by
Matthew Johnson
Carnegie Mellon University
Division of Statistics
Pittsburgh, PA 15213
masjohns@stat.cmu.edu
Abstract:
Multiple ratings of open-ended test items requiring subjective
scoring [e.g. essays, student artwork] have become increasingly
popular for many standardized tests [e.g. the Advanced Placement
exams of the Educational Testing Service]. The increasing
prevalence has posed a challenge in settings where item response
theory (IRT) is the primary method of analysis and/or scoring (Bock,
Brennan, and Muraki, 1998). Patz (1996) introduced and Junker and
Patz (1998) developed the Hierarchical Rater Model (HRM) in part to
address the difficulties created by IRT's strong conditional
independence assumptions. The HRM treats examinee responses to
open-ended items as {\em unobserved} discrete variables, and it
explicitly models the ``proficiency'' of raters in assigning
accurate scores as well as the proficiency of examinees in providing
correct responses. As a result, the HRM overcomes the problems of
double counting information in multiple ratings in much the same way
that traditional IRT overcomes the problem of double counting
information in multiple student responses---by introducing an
unobserved (latent) variable (the ``true'' item score) that explains
the dependence present in multiple ratings of the same student
response. We will describe the HRM in detail, compare it to
alternative approaches, and present several applications in which
the HRM is fitted using Markov Chain Monte Carlo techniques (e.g.
Patz and Junker, 1997a,b).
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by
John R. Lockwood III, Mark J. Schervish, Patrick Gurian, Mitchell J. Small
Carnegie Mellon University
Department of Statistics
Pittsburgh, PA 15213
jlock@stat.cmu.edu
Abstract:
The 1996 amendments to the US Safe Drinking Water Act (SDWA) mandate
revision of current maximum contaminant levels (MCLs) for various
harmful substances in public drinking water supplies. The
determination of a revised MCL for any contaminant must reflect a
judicious compromise between the potential benefits of lowered
exposure and the feasibility of obtaining such levels. This
evaluation is made as part of a
regulatory impact assessment (RIA) requiring detailed information
about the occurrence of the contaminant and the costs and
efficiencies of the available treatment technologies. Our work
focuses on the first step of this process, using a collection of
data sources to model arsenic occurrence in treatment facility
source waters as a function of system characteristics such as source
water type, location and size. We fit Bayesian hierarchical models
to account for the spatial aspects of arsenic occurrence as well as
to characterize uncertainty in our estimates. After model selection
based on cross-validation predictive densities, we use a national
census of treatment systems and their associated covariates to
predict the national distribution of raw water arsenic
concentrations. We then examine the relationship between proposed
MCLs and the number of systems requiring treatment and identify
classes of systems which are most likely to be problematic. The
posterior distribution of the model parameters, obtained via Markov
Chain Monte Carlo, allows us to quantify the uncertainty in our
predictions.
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by
Howard Seltman
Carnegie Mellon University
Division of Statistics
Pittsburgh, PA 15213
hseltman@stat.cmu.edu
Abstract:
Parameters of the biological rhythm of the hormone cortisol are
estimated using a compartmental model with a hidden stochastic process. The
physiological processes
of secretion and elimination are separately modeled, and the
net concentration is obtained by the convolution of secretion
and elimination. Basal and active rates of secretion are represented
as a two state hidden Markov chain. The transition probability
from basal to active states is modeled as a logit cosinor
curve. The development of a Markov chain Monte Carlo procedure
to sample the posterior distribution is presented. The use of a
compartmental model with a periodic hidden stochastic process offers
a new approach that directly allows testing of hypotheses relating
to alterations in the underlying physiological components
of a biological rhythm.
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by
Illaria DiMatteo and Joseph B. Kadane
Carnegie Mellon University
Division of Statistics
Pittsburgh, PA 15213
dimatteo@stat.cmu.edu
Abstract:
In an election on November 2, 1993, as a result of a first count,
candidate Joseph Zupsic defeated, by 36 vote margin, Dolores Laughlin
for the office of District Justice in Beaver County, PA. After a
second count, requested by the apparently defeated candidate, the
result of the election was reversed: Mrs. Laughlin beat Mr. Zupsic by
a 46 vote margin. How can it be determined if the change in votes
between the two counts was actually at random or a result of vote
tampering?
The data can be thought as a realization of an aggregate Markov chain
in which only the aggregate behavior of the ballots can be observed in
each precinct (namely the total number of ballots for each candidate
after each count). In estimating the transition probabilities of a
single ballot we augment the data. We also use the other races in the
election to determine the "normal" errors in the count-mechanism.
A hierarchical model is used to describe these data, and Markov Chain
Monte Carlo is used to estimate the posterior distribution of the
parameters in the model. The conclusions we draw lead us to believe
that vote tampering happened between the two counts. Furthermore the
conclusions of our model agree with the legal decision made in the
case.
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by
Sanjib Basu
Northern Illinois University
Division of Statistics
DeKalb, IL 60115
basu@niu.edu
Abstract:
Circular data represent directions in two-dimensions. Such data arise,
for example, in vanishing directions of pigeons when they are released
some distance away from their ``home''. The underlying scientific question
relates to how these birds orient themselves. Are they flying towards their
``home-direction''? Unimodality here would imply that pigeons have a
preferred vanishing direction and is a hypothesis of considerable
scientific interest.
As another example, several stations measure the mean wave direction
every hour which corresponds to the dominant energy of the period.
The wave directions depend on weather conditions, ocean currents and many
other natural factors. The daily variation of the wave directions is an
example of circular data on a 24-hour cycle. The hypothesis of
unimodality here would imply that there is an overall preferred
direction around which the daily variations of the wave directions are
distributed.
We propose a Bayesian
test for unimodality of circular data using mixtures of von-Mises
distribution as the alternative. The proposed test is
based on Markov Chain Monte-Carlo methodology. We illustrate its
application in several examples.
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