William F. Eddy - US grants

This research is designed to integrate Bayesian statistical inference and decision theory with modern computational and numerical methods. The core of the research program is the adaptation of methods for parallel/distributed processing of computation to problems in Bayesian statistics and decision theory. The research will have three principle directions: 1) theoretical development of the Bayesian methodology, 2) research into parallel/distributed computing algorithms, and 3) applications of numerical techniques to Bayesian problems. The methods, algorithms, and software to be developed for parallel/distributed processing will be important in a wide variety of theoretical and practical Bayesian problems. Areas of application will include hierarchical Bayesian modeling, sensitivity and robustness, sequential analysis with application in sequential process control, Bayesian methods for image reconstruction, and Bayesian inference for neural networks.

This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences. It is for the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required by several research projects, and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers, and with substantial cost-sharing from the institution submitting the proposal. This is an instance of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. The equipment in this project will be used to support research projects in the department of statistics at Carnegie- Mellon University, including Images Generated by Random Affine Maps; Statistical Modelling of Random Sets; Graphical Analysis of Parallel Algorithms; and Bayesian Methods for Image Reconstruction.

9508427 Eddy The Department of Statistics at Carnegie Mellon University will purchase an eight-node compute cluster for use as a small parallel computer. This equipment will be dedicated to support research in the mathematical sciences and will be used for several research projects, including in particular: 1. Functional Magnetic Resonance Imaging by William F. Eddy and Christopher Gen 2. Nested Analysis of Variance Directed by Evolutionary Graphs by Bernie Devlin and Kathryn Roeder 3. Dynamic Methods for Modeling Sea Height Anomalies by Ngai Hang Chan and Joseph B. Kadane

9418982 Cohen It is currently possible to acquire images of the brain so as to reveal the regions that are active while people are performing particular cognitive tasks. However, massive amounts of data (many successive images ) are produced from these neuroimaging studies, and it is not clear how to efficiently analyze all of the functional information that the data contain. With this award, a research group comprised of a psychologist, statistician, computer scientist and a radiologist (headed by Dr. Jonathan Cohen) will be developing new ways to analyze large sets of neuroimages. They will improve techniques for image reconstruction, expand available statistical tools for image processing, and implement these improvements on a supercomputer. This work should greatly advance the non-invasive analysis of brain function.

Proposal: DMS 9505007 PI(s): William Eddy, Chris Genovese Institution: Carnegie Mellon University Title: Statisitcal Methods for the Analysis of Functional Magnetic Resonance Imaging Data Abstract: This research involves the development of new statistical methods for the analysis and interpretation of functional Magnetic Resonance Imaging (fMRI) data. Such data can be viewed as the realization of a spatio-temporal process with a very complicated distributional structure. Models in current use are grossly simplified for both mathematical and computational expediency. The statistical challenges in constructing more realistic models are difficult and manifold. Many revolve around understanding the nature of the noise in the measurements and its effect on successfully detecting regions of neural activation. Noise in the data shows significant spatial and temporal correlations that depend strongly on how the data are collected. Outliers are common, and there are strong sources of systematic variation such as the subject's respiratory and cardiac cycles. Variances in the images depend nonlinearly on the means, and the observed absolute levels of activation tend to shift between sessions because of subject movement. Moreover, all of these difficulties occur for data collected from a single subject; the situation becomes much more complicated if comparisons across subjects are attempted. This research focusses on three general problems in the statistical analysis of fMRI data: 1. The characterization of the response to an activating stimulus in the fMRI signal and the use of this information to build more realistic models and make more precise inferences; 2. The development of robust procedures for identifying active regions that account for the complexity of the underlying spatio-temporal process; and 3. The construction of functional maps within a specified system of the brain (e.g., the visual system) and the use these maps for making predictiv e inference across subjects. Functional Magnetic Resonance Imaging (fMRI) is an exciting new technique that uses advanced technology to obtain images of the active human brain. The technique is of particular interest to cognitive neuropsychologists because of the unique perspective it offers into high-level cognitive processing in humans: areas of the brain that are activated by a stimulus or cognitive task ``light up'' in an fMRI image. This technology will thus play a critical role in understanding how the brain works; however, before this potential can be realized, significant statistical challenges in the interpretation and analysis of fMRI data must be overcome. For example, there is substantial uncertainty in the identification of neural activity from these images and in the attribution of that activity to particular cognitive processes. Moreover, there is a need for new methods of making statistical inferences of scientific interest from these large and complex sets of data. This research focusses on three broad aspects of the general problem: 1. Constructing models for the systematic components of the process that generates the data, 2. Studying and modeling the properties of the noise in the measurements so that analysis and inference can be made more precise, and 3. Developing new methods of inference for addressing interesting scientific questions with massive sets of data that arise from measurements over space and time.

Eddy, Genovese, & Lazar 9705034 Functional Magnetic Resonance Imaging (fMRI) is a powerful new tool for understanding the brain. With fMRI, it is possible to study the human brain in action and trace its processing in unprecedented detail. During an fMRI experiment, a subject performs a carefully planned sequence of cognitive tasks while magnetic resonance images of the brain are acquired. The tasks are designed to exercise specific cognitive processes and the measured signal contains information about the nature and location of the resulting neural activity. Neuroscientists use these data to help identify the neural processes underlying cognition and to build and test theoretical models of cognitive function. This is inherently a problem of statistical inference, yet the statistical methods for fMRI are still undeveloped. In this project, the statistical methodology for these large and complex data sets is advanced on three fronts: dealing with model response variation, developing better registration and acquisition methods, and analyzing spatial activation patterns. Functional Magnetic Resonance Imaging (fMRI) is a new tool that is currently being used to study the brain and the way it functions. Very large amounts of data, with considerable noise, are collected on neural activity while specific cognitive tasks are being performed. In this way, cognitive scientists hope to understand the processes underlying the way humans think. Statistical inference is a natural way of approaching this question. However, the complex nature of the data means that standard methods are not applicable and the methodologies used in fMRI for data analysis are still relatively undeveloped. The current project advances the statistical methodology for fMRI data by working in three directions. Brain response to a given task varies not only by location, but also in different replications of the same experiment. This source of variability is not taken into account by the models now in use. The first direction of the project incorporates this source of variation, resulting in more precise inferences. Subject motion during fMRI scanning is the focus of the second direction, while the third direction involves quantifying how spatial patterns of activation change over time. This allows the comparison of different individuals and groups.

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Eddy

At Carnegie Mellon University, the Department of Statistics and the Department of Mathematical Sciences will build on their complementary strengths to develop a joint, vertically-integrated program of education and research. Responding to national needs, the program will (i) train postdoctoral fellows for careers emphasizing research in settings that require versatility, (ii) aim to recruit and retain U.S. graduate students, avoiding excessive time to complete Ph.D.s while providing students with a high probability of success after graduation, and (iii) help increase the numbers of U.S. undergraduates, including women and minorities, who pursue advanced degrees in mathematical and statistical sciences. The program emphasizes cross-disciplinary research and understanding the needs of learners in a context of disciplinary advancement. Many of the activities grow from two previously-funded Group Infrastructure Grants to our respective departments, and from a very successful Undergraduate Summer Research Institute in Applied Mathematics. For instance, we plan to use the graduate support model from the infrastructure grant to Mathematical Sciences, we will expand the operation of the Summer Institute to include students from Statistics, and we will adapt for Mathematical Sciences some of the postdoctoral mentoring procedures that have worked well in Statistics.

Our evaluation of this training program will assess the following:
involvement of undergraduates in meaningful research experiences; its success in producing acceptable average time-to-degree for VIGRE graduate trainees; its effectiveness in expanding the mathematical horizons and career opportunities of students at both the undergraduate and the graduate levels, with particular focus on the graduate program; its effectiveness at the postdoctoral level in preparing VIGRE postdoctoral fellows for careers as professional mathematical scientists; its effectiveness in developing the communications skills of VIGRE participants; the effectiveness of the mentoring of undergraduate students, graduate trainees, and postdoctoral fellows; overall effectiveness of the research teams and other efforts to integrate research and education; the effectiveness of the partnership-in-training between the Departments of Statistics and Mathematical Sciences; and the degree of involvement of women and minorities.

Funding for this award is provided by the Division of Mathematical Sciences and the MPS Directorate's Office of Multidisciplinary Activities.

ABSTRACT

Project Summary

The department of Statistics at Carnegie Mellon University will purchase a cluster of 32 Dual processors computers which will be used for several research projects, including in particular:

1. Computational Astrostatistics by Larry Wasserman and Chris Genovese

2. Statistical Genetics and Evolutionary Simulations by Kathryn Roeder, Bernie Devlin and Larry Wasserman

3. Data Analytic Approach to Seismic Imaging by William F. Eddy, Mark Schervish and Pantelis Vlachos

4. Parallelized Spatio-temporal Analyses of Functional Magnetic Resonance Data by Chris Genovese, William F. Eddy and Nicole Lazar

The Principal Investigator will spend the 2005-2006 year studying magnetoencephalography in the Department of Neurological Surgery at the University of Pittsburgh Medical School. The plan is (i) to attend surgical conferences, surgeries, and lectures, much as a neurological resident; (ii) to become proficient at operating the magnetoencephalograph; and (iii) to develop statistical approaches to the analysis of magnetoencephalographic data.

This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).

Statistics curricula have required excessive up-front investment in statistical theory, which many quantitatively-capable students in ``big science'' fields initially perceive to be unnecessary. A training program at Carnegie Mellon will expose students to cross-disciplinary research early, showing them the scientific importance of ideas from statistics and machine learning, and the intellectual depth of the subject. Graduate students will receive instruction and mentored feedback on cross-disciplinary interaction, communication skills, and teaching. Postdoctoral fellows will become productive researchers who understand the diverse roles and responsibilities they will face as faculty or members of a research laboratory.

The statistical needs of the scientific establishment are huge, and growing rapidly, making the current rate of workforce production dangerously inadequate. The Department of Statistics at Carnegie Mellon University will train undergraduates, graduate students, and postdoctoral fellows in an integrated program that emphasizes the application of statistical and machine learning methods in scientific research. The program will build on existing connections with computational neuroscience, computational biology, and astrophysics.Carnegie Mellon will recruit students from a broad spectrum of quantitative disciplines, with emphasis on computer science. Carnegie Mellon already has an unusually large undergraduate statistics program. New efforts will strengthen the training of these students, and attract additional highly capable students to be part of the pipeline entering the mathematical sciences.

This project will conduct research on three basic issues of interest related to the conduct of censuses: privacy, costs, and response rates. The researchers will address the practical problems of insuring confidentiality and privacy while still producing useful data for public and private purposes. In terms of cost issues, the researchers will investigate the use of administrative records to create a basic census frame, saving the duplicated effort of gathering that same information repeatedly, as well as other possible uses of administrative records as part of the census. They also will investigate the use of online data collection as a substitute for the traditional mail-out/mail-back census-taking. With respect to response rates, the researchers will conduct experiments that implement new ways of encouraging participation in an effort to reduce the decline in (or perhaps even increase) response rates.

This research will explore the potential for a significant reduction in the costs of conducting the 2020 census by demonstrating how information already collected by the government can serve as a starting point for the census in lieu of having the Census Bureau collect that information anew as part of the decennial census process. By learning to effectively use the Internet for censal data collection, the research should lead to a higher initial response rate, and hence lower census costs overall, and a more accurate count. Better methods for confidentiality protection and privacy notification not only will instill greater public confidence in the Census Bureau, but they also will contribute to better response rates and greater census accuracy. All of the technical statistical tools developed by the project will have other uses, both public and commercial. The project's educational and training initiatives aim to (1) prepare an educated citizenry on census and related matters, (2) use research issues under study at CMU and elsewhere as components in courses, and (3) train a new generation of students to enable them to work in agencies such as the Census Bureau in a diverse set of capacities, including the most technically demanding ones. This activity is supported by the NSF-Census Research Network funding opportunity.

Statistics curricula have required excessive up-front investment in statistical theory, which many quantitatively-capable students in ``big science'' fields initially perceive to be unnecessary. A research training program at Carnegie Mellon exposes students to cross-disciplinary research early, showing them the scientific importance of ideas from statistics and machine learning, and the intellectual depth of the subject. Graduate students receive instruction and mentored feedback on cross-disciplinary interaction, communication skills, and teaching. Postdoctoral fellows become productive researchers who understand the diverse roles and responsibilities they will face as faculty or members of a research laboratory.

The statistical needs of the scientific establishment are huge, and growing rapidly, making the current rate of workforce production dangerously inadequate. The research training program in the Department of Statistics at Carnegie Mellon University trains undergraduates, graduate students, and postdoctoral fellows in an integrated environment that emphasizes the application of statistical and machine learning methods in scientific research. The program builds on existing connections with computational neuroscience, computational biology, and astrophysics. Carnegie Mellon is recruiting students from a broad spectrum of quantitative disciplines, with emphasis on computer science. Carnegie Mellon already has an unusually large undergraduate statistics program. New efforts will strengthen the training of these students, and attract additional highly capable students to be part of the pipeline entering the mathematical sciences.

This award provides support for a Workshop on Statistical Analysis of Neuroimaging Data for Social and Behavioral Science Research, to be held during September 2011 in the Washington, DC metropolitan area. The workshop will convene a multidisciplinary group of experts in magnetic resonance imaging, statistics, and the social and behavioral sciences to address questions concerning the nature of the analysis of fMRI data and the nature of social and behavioral science questions that reasonably can be answered by fMRI experimentation. In particular, the workshop will focus on the following issues: (1) What experimental designs are appropriate and what can or cannot be learned with these designs? and (2) What are "proper" statistical analyses and what statistical methods are inappropriate?

Since the mid-1990s, neuroimaging has moved from being almost exclusively a clinical science to an experimental tool with widespread application in the social and behavioral sciences. There is, however, no general agreement on how to analyze data from neuroimaging experiments. This workshop will facilitate a much needed dialogue on the interplay between neuroimaging techniques, data analysis, and the social and behavioral science questions that can be addressed with these approaches. Plans for dissemination to the broader research community include a web site for the workshop and a collection of papers in a neuroscience journal.