Greetings, and apologies for cross-posting.
If you could please pass this on to anyone you know who may be interested
in it, that would be terrific.
Many thanks and best wishes, David Draper
Short Course
Intermediate and Advanced Applications of Bayesian Methods: Bayesian
Hierarchical/Multilevel Modeling
Presenter
Professor David Draper
Chair, Department of
Applied Mathematics and Statistics
Baskin School of Engineering
University of California
1156 High Street
Santa Cruz CA 95064 USA
email [log in to unmask]
web www.ams.ucsc.edu/~draper
phone US (831) 459 1295, nonUS +1 831 459 1295
fax US (831) 459 4829, nonUS +1 831 459 4829
Venue
A continuing education (CE) course offered as part of the 2003 Joint
Statistical Meetings (JSM) in San Francisco, CA (6 hours of CE credit
available for participation in the course)
Date
Tuesday 5 Aug 2003, 8.15am - 4.15pm
Location
Hotel Nikko San Francisco, 222 Mason Street, San Francisco, CA
Course Fee (US$)
Students $200, ASA members $325, non-members $415 (if paid by 18 Jul 2003)
To Register
The code for this CE course is CE2003_21C -- you can go to
www.amstat.org/meetings/jsm/2003/
to register electronically (you don't need to register for the other parts
of the JSM to attend a CE course, but if you're going to the JSM anyway
it's straightforward to include one or more CE courses in the registration
process).
American Statistical Association (ASA) Contact Information
In case you have difficulties with the electronic registration process, or
if you have any other questions, the ASA may be contacted as follows:
American Statistical Association
1429 Duke Street
Alexandria VA 22314-3415 USA
phone 703-684-1221
toll-free 888-231-3473
fax 703-684-2037
email [log in to unmask]
Abstract
This course provides coverage of intermediate and advanced topics arising
in the formulation, fitting, and checking of hierarchical or multilevel
models from the Bayesian point of view.
Hierarchical models (HMs) arise frequently in four main kinds of
applications:
* HMs are common in fields such as health and education, in which
data -- both outcomes and predictors -- are often gathered in a nested
or hierarchical fashion: for example, patients within hospitals, or
students within classrooms within schools.
HMs are thus also ideally suited to the wide range of applications in
government and business in which single- or multi-stage cluster samples
are routinely drawn, and offer a unified approach to the analysis of
random-effects (variance-components) and mixed models.
* A different kind of nested data arises in meta-analysis in, e.g.,
medicine and the social sciences.
In this setting the goal is combining information from a number of
studies of essentially the same phenomenon, to produce more accurate
inferences and predictions than those available from any single study.
Here the data structure is subjects within studies, and as in the
clustered case above there will often be predictors available at both
the subject and study levels.
* When individuals -- in medicine, for instance -- are sampled
cross-sectionally but then studied longitudinally, with outcomes
observed at multiple time points for each person, a hierarchical data
structure of the type studied in repeated-measures or growth curve
analyses arises, with the readings at different time points nested
within person.
* Hierarchical modeling also provides a natural way to treat issues of
model selection and model uncertainty with all types of data, not just
cluster samples or repeated measures outcomes.
For example, in regression, if the data appear to exhibit residual
variation that changes with the predictors, you can expand the model
that assumes constant variation, by embedding it hierarchically in a
family of models that span a variety of assumptions about residual
variation.
In this way, instead of having to choose one of these models and risk
making the wrong choice, you can work with several models at once,
weighting them in proportion to their plausibility given the data.
The Bayesian approach is particularly effective in fitting hierarchical
models, because other model-based methods -- principally involving maximum
likelihood -- often do not fully capture all relevant sources of
uncertainty, leading to over-confident decisions and scientific
conclusions.
In this course the basic principles of Bayesian hierarchical modeling will
be reviewed, with emphasis on practical rather than theoretical issues,
and intermediate- and advanced-level ideas will be illustrated with real
data drawn from case studies involving complicated applications of HMs in
cluster sampling, longitudinal data analysis, and mixture modeling.
The course is intended for applied statisticians with an interest in
learning more about intermediate and advanced topics in hierarchical
modeling in general, and the Bayesian analysis of such models in
particular.
An understanding of probability and statistics at the level typically
required for an M.S. degree in statistics provides sufficient mathematical
background.
This course is intended to be a follow-on from an introductory treatment
of Bayesian statistics, so I will assume that participants have background
in Bayesian methods and hierarchical modeling at the level (for instance)
of the first six chapters of the textbook by Gelman et al. (Bayesian Data
Analysis, 1995) or equivalent.
An example of an equivalent background would be for participants to have
completed the basic Bayesian methods short course to be offered by Mike
Escobar at the 2003 JSM, which will be given on Sunday 3 Aug 2003; JSM
participants who want to go into more depth on Bayesian methods could take
the Escobar course first and then my course.
Target Audience
The principal target audience includes applied statisticians (1) who work
with data possessing a hierarchical or multilevel character (clustered
and/or longitudinal) on a regular basis, or who wish to do so; (2) who
wish to extend their experience in the contemporary fitting of
random-effects and mixed models, in meta-analysis and other settings; (3)
who wish to improve their skills in formulating and fitting mixture
models; and (4) who wish to learn more about current methods for coping
with problems of model selection and model uncertainty (with all kinds of
data, not just cluster samples).
Application areas in which hierarchical modeling occurs frequently include
policy analysis and other governmental activities, agriculture, medicine
and health, education, and biology.
Others who may be interested in this course include applied and
methodological workers who wish to learn more about (5) comparisons in
complexity and performance between Bayesian and frequentist methods and
(6) Markov Chain Monte Carlo (MCMC) techniques and how to ensure that they
work well in practice.
There are no formal mathematical prerequisites, but a working knowledge of
probability and statistics at the M.S. level (from such books as Hogg and
Craig, Bickel and Doksum, or Casella and Berger) -- particularly the
ability to conceptualize and manipulate conditional probabilities -- will
be desirable, and upper-division undergraduate or M.S.-level study in
linear models will also be helpful.
Tentative Syllabus/Outline
8:15 -- 9:00am (review of Bayesian modeling). Probability as
quantification of uncertainty about observables. Prior, posterior, and
predictive distributions for parameters and observables. Comparison with
frequentist modeling. Case studies: Diagnostic screening for HIV,
estimation of a physical constant in a measurement error model.
9:00 -- 9.45am (review of hierarchical models (HMs) for combining
information). Exchangeability as a Bayesian concept parallel to
frequentist independence. Formulating hierarchical models for quantitative
outcomes from scientific context. Appropriate prior distributions for
multilevel models. Case study: Educational meta-analysis of effects of
teacher expectancy on pupil performance.
9.45 -- 10:15am Break
10:15 -- 11:00am (review of Bayesian computation). Markov Chain Monte
Carlo (MCMC) methods. User-friendly implementation of MCMC via WinBUGS and
MLwiN, the two most widely available Bayesian hierarchical modeling
packages. MCMC diagnostics. Case study: Random-effects Poisson regression
models in a controlled trial of in-home geriatric assessment.
11:00am -- noon (review of diagnostics, model checking, and model
elaboration). Bayesian cross-validation as an approach to diagnostics:
comparing outcomes from omitted cases with their predictive distributions
given the rest of the data. The Deviance Information Criterion (DIC) for
model choice. Expansion of a simple model that does not satisfy all
diagnostic checks, by embedding it in a richer class of models of which
it's a special case. Case study: Continuation of geriatric example.
noon -- 12:45pm Lunch
12:45 -- 1:45pm (HMs for clustered data). The model-based approach to the
analysis of cluster samples. Random-effects and mixed models from the
Bayesian viewpoint. Case study: Hierarchical profiling of universities by
comparing observed and expected student dropout rates.
1:45 -- 2:45pm (HMs for longitudinal data). Repeated-measures and
growth-curve data analysis. Case study: Tumor growth rates as a function
of covariates in lung cancer investigations.
2:45 -- 3:15pm Break
3:15 -- 4:15pm (HMs for mixture modeling). Hierarchical modeling with
latent variables as an approach to mixture modeling. Bayesian
nonparametric inference and prediction with Polya trees. Case study: Risk
assessment in nuclear waste disposal.
As time permits, examples from small-area estimation and spatial data
analysis will also be presented.
At several times throughout the day the following themes will also be
emphasized:
Conclusions and caveats; warnings on the unwary use of HMs; several
examples of poor HMs and how to improve them; Bayes does not equal free
lunch; but also: situations in which Bayesian estimates can out-perform
likelihood-based procedures using repeated-sampling criteria.
Learning Outcomes/Performance Objectives
* Participants will improve their skills at translating scientific and
decision-making problems involving nested or clustered data into
appropriate hierarchical models (including random-effects and mixed
models, repeated-measures models, and mixture models), and will also
become more proficient -- with any kind of data, not just a cluster
sample -- at embedding a given model hierarchically in a richer model
class, as a way to realistically approach issues of model selection and
model uncertainty;
* Participants will gain a deeper understanding of methods for computing
posterior and predictive distributions for quantities of interest
arising in the hierarchical models formulated in (1); and
* Participants will learn new methods for examining the results of the
model-fitting in (2) for weaknesses and for sensitivity to modeling
assumptions.
By taking part in this course, participants will develop and/or extend
facility in
* Formulating appropriate hierarchical (random-effects and/or mixed)
models for nested outcomes (both qualitative and quantitative) in
meta-analyses, investigations involving cluster samples, longitudinal
studies, and mixture modeling, and in situations with predictor
information available at some or all levels of the hierarchy;
* Using Bayesian reasoning and MCMC methods to compute posterior
distributions for parameters of greatest interest in a given
hierarchical model;
* Diagnosing problems with a given hierarchical model by looking for
discrepancies between predictive distributions for observables and the
actual values the observables take on, and using DIC to guide model
choice; and
* Hierarchically expanding an existing model (for all kinds of data, not
just cluster samples) which does not pass all diagnostic checks, by
embedding it in a richer model class of which it's a special case.
Content and Instructional Methods
I will help participants achieve the above learning outcomes by exploring
a variety of case studies -- drawn from education, health policy,
medicine, gerontology, and risk assessment -- with emphasis on the
practical interaction between scientific, decision-making, and statistical
considerations.
Extensive details required for carrying out the analyses will be provided
in the course materials.
I will offer real-time computer demonstrations to participants, using the
two major Bayesian hierarchical modeling packages now most widely
available (WinBUGS and MLwiN), with hardcopy of these real-time sessions
so that participants can recreate them later.
Time permitting, the fitting of hierarchical models in SAS PROC MIXED,
S-PLUS, and Stata will also be addressed.
About the Presenter
David Draper is a Professor in, and Chair of, the Department of Applied
Mathematics and Statistics in the Baskin School of Engineering at the
University of California, Santa Cruz (UCSC).
He did his Ph.D. work at the University of California, Berkeley, finishing
in 1981, and he has since taught and done consulting and public policy
research at the University of Chicago (1981-84); the Rand Corporation
(1984-91); the University of California, Los Angeles (1991-93); the
University of Bath, UK (1993-2001); and UCSC (2001-present), with a
sabbatical visit to the University of Washington in 1986.
He is a Fellow of the Royal Statistical Society and has served as
Associate Editor for the Journal of the American Statistical Association
(Theory and Methods, 1988-91; Applications and Case Studies, 1988-94) and
for the Journal of the Royal Statistical Society, Series B (1995-1998).
From 2001 to 2003 he has served and is serving as President-Elect,
President, and Past-President of the International Society for Bayesian
Analysis (ISBA).
His research is in the areas of Bayesian inference and prediction, model
uncertainty and empirical model-building, hierarchical modeling, MCMC
methods, and Bayesian nonparametrics, with applications mainly in health
policy, education, and environmental risk assessment.
He is the author or co-author of 4 books, 4 book chapters and 49 research
papers and invited discussions in leading statistics and applications
journals, including 3 discussion papers on exchangeability, hierarchical
modeling and MCMC in the Journal of Educational and Behavioral Statistics
and the Journal of the Royal Statistical Society (Series A and B).
From 1998 to the present he has served as a statistical advisor to the UK
Higher Education Funding Council for England on the use of hierarchical
models to construct performance indicators (measures of quality) for
British universities, and from 1995 to the present he has served as
principal advisor to 3 Masters students and 5 Ph.D. students whose
dissertations were devoted to aspects of Bayesian hierarchical modeling.
He has been nominated for teaching awards at every university in which he
has taught (e.g., he was the recipient of the Quantrell Award for
Excellence in Undergraduate Teaching at the University of Chicago in
1984), and he has given two extended courses, of six and 18 hours, on
Bayesian statistics and hierarchical modeling at the Universities of Bern
(October 1994) and Neuchatel (June 1995, 1996, 1997) in Switzerland.
In 1997 and 1998 he gave 1- and 2-day courses on Bayesian hierarchical
modeling at the Anaheim and Dallas JSMs; his 1997 course won an ASA
Excellence in Continuing Education award.
He has a particular interest in clearly expositing methodological ideas,
in the context of applied case studies, to diverse audiences.
=============================================================================
Professor David Draper
Chair, Department of
Applied Mathematics web http://www.ams.ucsc.edu/~draper/
and Statistics email [log in to unmask]
Baskin School of phone US (831) 459 1295, nonUS +1 831 459 1295
Engineering fax US (831) 459 4829, nonUS +1 831 459 4829
University of California
1156 High Street departmental web pages www.ams.ucsc.edu
Santa Cruz CA 95064 USA
Interesting quotes, number 24 in a series:
The end is in the beginning; and yet you go on.
-- Samuel Beckett
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