David Draper (last update 28 October 2001)
(0. Under the pressure of other commitments this web page has fallen somewhat out of date and is in serious need of updating; my apologies.)
1. Recent and upcoming events and news items of possible interest:
AMS is offering a new course next quarter (beginning in the week of 26-30 March 2001) on Bayesian statistical methods and reasoning, which I will be teaching.
This is a potentially exciting topic to both undergraduate and graduate students with a variety of interests in science and engineering, because
Partly because (i) we are new, (ii) I am unfamiliar with how to market such courses, and (iii) I may have set the initial prerequisites too high given that there has not been much teaching of statistics on campus in the past, the pre-enrollment for this course is very low, and it is in danger of being canceled.
I am going to be very liberal in interpreting the "permission of instructor" prerequisite as a way of inviting all students who might be interested to come to the first few classes -- I will see who shows up and what their backgrounds are, and will tailor the class to the enrollment.
If you wish to enroll in this class, please contact me by email at draper@ams.ucsc.edu or in person (Baskin Engineering 147) -- I have lots of permission codes.
A description of the course follows.
This course will provide an introduction to Bayesian statistical methods for inference and prediction.
Statistics is the study of uncertainty - how to measure it, and what to do about it. As such, it is of potential interest in many (virtually all?) aspects of science and decision-making. Of the two main ways to quantify uncertainty -- involving relative frequency and subjective (Bayesian) notions of probability -- the second way is more flexible and general, but for a long time the Bayesian approach was limited in applications by an inability to perform high-dimensional numerical integrations. With the advent of powerful computers and new simulation-based techniques over the past 10 years, the computing problem is now solved, and there has been a revolution in Bayesian methods and applications.
The course will be methodological but will be guided by a series of real-world case studies. The first half of the course will involve symbolic mathematical calculations in the computer package Maple, and statistical analyses and graphics in the package R; contemporary Bayesian computation using the package WinBUGS will feature prominently in the second half.
The instructor, who has won or been nominated for major teaching awards at four leading universities in the US and England, will survey the background of the initial participants in the course in mathematics and probability to decide how the course should be run for maximal benefit of the participants. He intends to provide a course that will be interesting and profitable for a variety of students at both the undergraduate and graduate levels.
The week-by-week breakdown of topics to be covered is as follows.
The main textbook for the course will be
There will be homework assignments (more like small take-home tests) given out in weeks 2, 4, 6, and 8 and due one week later; these will blend paper-and-pen, symbolic computing, statistical and MCMC calculations. A take-home final exam will be assigned in week 9 and due at the end of the final examination period.
At this year's Interface 2001 meeting in southern California, I will give a two-day short course on Bayesian hierarchical modeling, with the first day on introductory and intermediate topics and the second day on advanced issues. This is scheduled to take place on (Mon-tue) 11-12 June 2001.
3. Personal information
The intended audience for the book is methodological and applied statisticians who wish to learn (more) about the formulation and fitting of hierarchical (multilevel) models from the Bayesian point of view.
An understanding of probability at the level typically required for a master's degree in statistics would provide ample mathematical background for reading the book. I have taught subsets of the draft material successfully to groups including British final-year undergraduates, American PhD students, and PhD-level researchers enrolled in short courses (including an award-winning course at the Anaheim Joint Statistical Meetings in 1997), and the book has also proven useful for self-study by researchers and graduate students in a variety of disciplines (including statistics). No previous experience with Bayesian methods is needed -- all relevant ideas are covered in a self-contained fashion.
The draft manuscript PostScript file is about 1.5Mb, and when printed you get 183 pages: Contents and Preface (pp. i-xiv), Chapter 1 (pp. 1-46), Chapter 2 (pp. 47-122), some placeholder stuff you can avoid printing (pp. 123-138, 169), Appendix 2 (pp. 139-160), and References (pp. 161-168).
The first chapter (46 pages) provides a standalone introduction to Bayesian modeling in the context of two case studies, and the second chapter (76 pages) offers an in-depth look at Markov Chain Monte Carlo (MCMC) methods from first principles, also based on two case studies. The writing style is informal; the main text is not very mathy, but each chapter is supplemented by extensive endnotes giving additional formalism and details.
Appendix 2 contains S+, BUGS, Maple, and C programs for conducting the analyses in Chapter 2; these programs are also available for downloading here as a 36Kb text file. Chapter 2, when combined with computer work based on the code supplied here, might make a nice MCMC tutorial to supplement any other coverage you may have on this topic, and Chapter 1 might serve as a gentle introduction to Bayes for advanced undergraduates or beginning grad students.
The only things I ask in return for the free use of these materials in your teaching are (a) that you email me giving details (class or tutorial size and name, level of students) of both (i) when and where you have used the book and programs, and (ii) any errors or problems you encounter, or other comments you wish to pass on; and (b) that - if you like this material - you consider buying a copy of the finished book, which (I hope) will be published within the next 12 months!
One-day workshops on MCMC methods in multilevel modeling were given by David Draper (University of Bath) and Bill Browne (Institute of Education, University of London) on April 6 and October 29, 1998 at the Institute of Education, using the new Windows version of MLn (MLwiN), which has recently been released. The workshops were offered in conjunction with the Multilevel Modelling Project, led by Harvey Goldstein.
The workshops combined methodology discussion with real-time hands-on computing experience, and there was also an opportunity for participants to submit their data sets for inclusion as case studies for interactive analysis in the afternoon session.
The intended audience was multilevel/hierarchical modelers (of varying levels of experience, from not much to quite a lot) who wish to learn about Markov Chain Monte Carlo (MCMC) Bayesian methods and their implementation in MLwiN, and people interested in learning about the new interactive model specification, fitting, and diagnostic capabilities of the new Windows version of MLn also found the workshops worthwhile. Bill Browne and I are the co-developers of the MCMC functionality in MLwiN.
We are interested in giving future workshops of this type, and are open to suggestions on location and timing. If you would like to discuss this possibility, or for further details, please email Bill Browne, or phone me at +44 (0) 1225 826222. The MLwiN software would be available for a discount as part of coming to the workshop.
A tentative program for the day is as follows:
The cost of the workshop would be as follows:
I have recently given two one-day short courses on Bayesian hierarchical modeling, based on the book described in 1.1 above, at the Dallas Joint Statistical Meetings in August 1998, through the American Statistical Association (ASA) Continuing Education program.
The first day was an invited short course, offered at an introductory/intermediate level -- it essentially repeated the course I gave in Anaheim in 1997, which won an ASA Excellence in Continuing Education award. No previous exposure to Bayesian methods was needed in this first course -- all ideas were covered in a self-contained fashion. Topics for the first course included (1) an introduction to Bayesian modeling, (2) MCMC methods from scratch, (3) formulation of hierarchical models (HMs) based on the scientific/decision-making context, and (4) diagnostics for HMs.
The second day covered more advanced topics, including (1) random-effects and mixed models, (2) Bayesian nonparametric inference with Polya trees, and (3) HMs as an approach to model selection and dealing with model uncertainty. Each day can be taken in a standalone fashion, or people can come to both days if they want to.
I am interested in giving these short courses again in the future. If you would like to suggest a time, place, and audience, please email me.
1.4 INTERNATIONAL WORKSHOP ON STOCHASTIC MODEL BUILDING AND VARIABLE SELECTION Duke University, Durham NC October 9 and 10, 1997 |
A Workshop whose goal was bringing together researchers interested in novel approaches to computer-based and/or simulation-based aids to model building.
The program of the Workshop included both talks and poster presentations. For lists of the speakers and participants, practical details, and other information see this web page; if you have questions please email Giovanni Parmigiani or me.
Date and time: 14 May 1997, 2-6.50pm.
Place: headquarters of the Royal Statistical Society (RSS), 12 Errol Street, London EC1Y 8LX England (voice +44-171-638-8998, fax +44-171-256-7598, email rss@rss.org.uk).
Four papers (available for downloading) by international teams of leading researchers in survey sampling, together with invited and contributed discussion and rejoinder. For more information see this web page or email me.
I am a Professor in, and Head of, the Statistics Group in the Department of Mathematical Sciences. My phone number is +44-1225-826222; fax is +44-1225-826492; email is d.draper@maths.bath.ac.uk. My postal address is Statistics Group, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, England.
Before coming to Bath I studied for a BSc in mathematics at the University of North Carolina/Chapel Hill (1970-74) and a PhD in statistics at the University of California/Berkeley (1975-81); worked at IBM in New York (1974-75); and taught and did research at the University of Chicago (1981-84), the RAND Corporation (1984-91), and UCLA (1991-93), with brief sabbatic and consultant stints at the University of Washington (1986) and AT&T Bell Labs (1987). Since arriving in Bath I have also done some teaching at the University of Neuchâtel in Switzerland, and given short courses on Bayesian hierarchical modeling at the joint meetings of the American Statistical Association and the Institute of Mathematical Statistics.
Philosophically I am some kind of de Finetti-style Bayesian, meaning that for me
To me it's OK to supplement contextual information from experts with data analysis in forming your exchangeability judgments, as long as you keep yourself honest by not using the data twice in the process.
In practice for me this often means employing predictive calibration: holding out some of the data from the modeling and seeing where the observed outcomes in the held-out data fall in their respective model-based predictive distributions. If this kind of predictive calibration fails, then you have to go back and change the model (which includes the possibility of changing the ``prior'') until you are well-calibrated.
I see this as a kind of fusion of the best of Bayesian and non-Bayesian reasoning: (1) Bayes by itself (when done right) guarantees internal but not (2) external consistency, which involves asking inherently frequentist questions (how often do my predictive intervals include the observed outcomes?).
This philosophy has implications both in research and teaching, which I am currently refining. If you disagree with the views above and would like to talk about it, please email me.
2.5 Funded Research Projects
I have just finished working with Dr. Ryan Cheal (Bath) and partners at the Environmental Institute, Joint Research Center (Ispra, Italy), CIEMAT (Madrid, Spain), and the University of Stockholm (Sweden) on GESAMAC, a three-year EC-funded environmental project exploring the likely effects on the geosphere from possible future failure of underground containment vessels for spent nuclear fuel.
Ryan and I were helping to quantify all relevant sources of uncertainty (from model input scenarios, model structural assumptions, model parametric variability, and predictive inaccuracy) in forecasts of radiologic dose arising from containment vessel failure. The EC has made the working documents from this project confidential, but two papers now in the open literature are available: Draper (1997), Model uncertainty in stochastic and ``deterministic" systems, Proceedings of the 12th International Workshop on Statistical Modeling, Biel, July 1997, Schriftenreihe der Osterreichischen Statistichen Gesellschaft, 5, 43-59; and Draper et al. (1998), Scenario and parametric uncertainty in GESAMAC: A methodological study in nuclear waste disposal risk assessment, Computer Physics Communications, forthcoming.
If you have interests in this area I would like to start a dialogue with you; please email me.
I have also just finished working with Dr. Russell Bowater and partners at the Office for National Statistics, the Department of Social Statistics at the University of Southampton, and Statistics Sweden on a one-year project funded by Eurostat, to develop and test methodology to better account for all sources of uncertainty in complex business surveys of the type routinely undertaken by EC member countries.
We reviewed and tested methodologies for
I also have a basic interest in the teaching of statistics at the BSc, MSc and PhD levels. I have taught at Berkeley, Chicago, RAND, Seattle, UCLA, Bath, Neuchâtel, and the American Joint Statistical Meetings on introductory statistics, design of experiments, sample surveys, multivariate methods, computationally intensive inference, linear models, statistical modeling, Bayesian inference and prediction, and Bayesian hierarchical modeling.
I believe that three principles should govern the teaching of statistics at all levels:
What works for me is (a) to reason in a Bayesian way when formulating my inferences and predictions and (b) to reason in a frequentist way when evaluating their quality, through predictive calibration (see the section on philosophy above).
There are certainly other ways to look for the best in Bayes and non-Bayes; I am sure you have your own (strong) views on the subject, and I would be interested to hear them.
Many inferential questions can usefully be rephrased in predictive terms, e.g., if you are a physician the key medical question is often not (whether treatment A is better on average than treatment B in some population) but (how much different the outcome would be under the two treatments for the patient in front of you). Given all of this, why do we spend so little teaching time on prediction?
This four-step approach echoes the process by which the methods were originally developed, which encourages people to see how ideas are discovered in the first place. It is especially good to cover step (2) in an interactive way, asking people to help suggest ideas for what to do next and exploring rather than condemning dead-ends, because in practice the discovery process itself often proceeds by learning what is wrong with each of a series of partial failures.
I am currently looking for PhD students to work with me on the following topics:
The Bayesian solution is essentially to deal with model uncertainty in the way that a nuisance parameter would be treated, by integrating over it as in the following three-step program (Draper D (1995), Assessment and propagation of model uncertainty (with discussion), Journal of the Royal Statistical Society Series B, 57, 45--97):
In both instances process is difficult and expensive to measure, so interest has begun to focus on a less costly input-output approach to quality assessment, in which institutional outcomes are compared after adjusting for differences in inputs. In the case of hospitals this may take the form of a contrast between observed and expected mortality rates, given how sick patients are when they arrive at the hospital; in schools value-added computations examining A-level results (from standardized tests taken in the last year of high school) after accounting for GCSE scores (from another set of standardized tests taken one year earlier) have begun to emerge. Bayesian hierarchical modeling that is explicitly tailored to the multilevel structure of the data (patients nested within hospitals, students within classrooms within schools) plays a central role in this approach to quality assessment.
Projects available in this area include (a) the solution of technical problems posed by the hierarchical modeling of massive data sets and (b) explicit attempts to guide public policy by using such modeling to suggest optimal data collection strategies and optimal allocation of resources between input-output and process-only quality assessments.
This project involves the theory and application of MCMC in the context of Polya trees - and other approaches to non-parametric Bayesian inference - in a way that is responsive to actual applied prior knowledge on, e.g., unimodality, tail behavior, and moments of CDFs (on the one hand) and monotonicity and smoothness of regression surfaces (on the other), in the context of theory, simulations, and real case studies. I have recently used Polya trees to solve a consulting problem for AEA Technologies in risk assessment arising from nuclear waste disposal, and I am eager to explore the practical limits of this modeling strategy.
One way out of this difficulty involves the sort of Bayesian nonparametric analyses described in the previous project. In this project another approach, out-of-sample predictive validation, will be used to overcome the central problem posed by Cromwell's Rule. The idea is to cross-validate the modeling process - by setting aside some data and using a range of models fitted to another subset of the data to predict the set-aside observations - but in such a way as to obtain an honest estimate of predictive accuracy of the composite modeling process. Theory, simulations, and case studies will be used to explore the strengths and limitations of this approach.
My wife is Dr. Andrea Steiner, a Senior Lecturer in gerontology and health policy analysis in Social Sciences and Geriatric Medicine at the University of Southampton. We live in an old stone house in Limpley Stoke, a nice village on the river Avon near Bath, with a canal, some good pubs, and some excellent hill-walking nearby. I now know a lot more about real ale than I did six years ago.