Mario Peruggia - US grants

The Department of Statistics at The Ohio State University intends to purchase a high-resolution color workstation and imaging system to be dedicated to the support of research in the mathematical sciences. The equipment will be used in several new and ongoing research projects, including in particular: 1) Graphical Methods for High Dimensional Stochastic Dynamical Systems by L. Mark Berliner 2) Dynamic Analysis of Hierarchical Bayes Models by Mario Peruggia and Thomas Santer 3) Dynamic Graphical Predictions in Multistate Survival Models by John Klein 4) Confidence Ellipsoids for Bioequivalence by Jason Hsu All Four projects require the use of a high-resolution color graphics system with the ability to make, display and record animated sequences and still images.

This research will develop accurate and powerful Bayesian modeling and computational methods for the problem of response time (RT) analysis. Although Bayesian techniques are well established in other fields, social scientists very rarely use them because they require a considerable investment in computational resources as well as additional statistical training. The project will develop a number of strategies that will improve the analysis of RT data, including analyses that consider theories about how RTs are produced and new procedures that can help untrained practitioners use Bayesian methods without too much inconvenience. The study also undertakes a program of education and dissemination to improve the overall quality of statistical analyses of RT data. Thus, this research will result in new and better statistical procedures specific for RT (and similar chronometric) data.

The importance of this project is considerable. How well a person performs a task is often evaluated by way of how quickly he or she can respond during the task. Measurements of RTs are important for both theoretical and pragmatic reasons. Theoretically, RTs are used to test hypotheses about cognitive structure, the ways in which people use and process information, and how changes in the environment influence human behavior. Pragmatically, RTs are important for evaluating human performance in many areas. They assist machine interface design decisions, such as the optimal way to present information to a pilot or the best place where to put a turn signal lever. They are also used in medicine; diagnoses of some organic brain disorders such as Alzheimer's disease or Attention Deficit Hyperactivity Disorder can be informed by a patient's RTs on certain kinds of tests. Many of the statistical procedures used to test hypotheses based on RTs are suboptimal. They depend on oversimplifying assumptions about RT data that are usually incorrect, and consequently the inferences that are made about RTs collected in different environments can be faulty. This project will result in more accurate characterization of RT data and therefore improved decision making about human capabilities and disease.

Psychologists and marketing experts have different theories about why people make the choices they do. While psychological theories more accurately describe individual human choice behavior in simple circumstances, they do not typically consider the range of variables, such as product features, consumer factors, vendor strategies, that marketing theories must be able to handle. Nor do they consider the fact that individuals' behaviors interact to form and influence marketplace demand. In this project, psychologists, marketing experts, and statisticians will collaborate to merge these theories. This collaboration will result in a deeper understanding of consumer behavior through better marketing theories and more complete psychological theories of human choice. Statistics is at the heart of the research, providing the unifying conceptual instrument for combining the varied theories and data sets through models such as the hierarchical Bayesian model. The hierarchical Bayesian structure allows one to describe simultaneously and coherently individual and aggregate behavior and to combine the disparate psychological and marketing theories and data. The Bayesian nature of these models allow one to adjust for known effects, even in experiments of modest size. The models also allow one to move from experimental settings to forecasting behavior in the marketplace.

Human behavior reflects a complex, multi-stage process that begins with the allocation of an individual's resources to affect his or her environment and to improve his or her state of being. This research will improve understanding of human behavior both in the marketplace and in general. The research will take place at the nexus of the three disciplines, statistics, marketing and psychology, with benefits to all three fields. The project has a strong educational emphasis and will provide the many students involved with a unique opportunity for cross-disciplinary training. This will aid them in their careers in academics, industry, or government. This award was supported as part of the Fiscal Year 2004 Mathematical Sciences priority area special competition on Mathematical Social and Behavioral Sciences (MSBS).

The degree of complexity and sophistication in modern statistical models has various consequences. This project addresses two important, related aspects. First, how can one assess if specific features of a model provide an accurate representation of the phenomenon under study? Further, if some features are identified as problematic, in what direction should they be modified to improve the fit of the model? Second, as models become more complicated, fitting the models also becomes harder. It would be a mistake to think that raw computing power is all that is needed to keep pace with the increasing complexity. Novel algorithmic approaches are needed to tackle the challenges posed by modern modeling practices. Old techniques used on more powerful computers might only run longer, without producing the desired output. This project establishes some important and novel connections between the theoretical properties of Bayesian hierarchical models and some other areas of statistics, such as time series analysis and cluster analysis, leading to advances in the area of model diagnostics and elaboration and to the development of an effective class of algorithms for fitting Bayesian mixture models.

Recent advances in computational resources have afforded modelers unprecedented opportunities to describe real life and natural phenomena in very realistic terms. As reality is inherently complex, realistic models tend to be highly sophisticated. The need for accurate and reliable modeling cannot be overemphasized. Public
policy decisions are routinely made on the basis of probabilistic models that forecast economic and social indicators, predict environmental factors, assess the potential for disease outbreak, etc. Small deficiencies in the models and little estimation inaccuracies can have consequences that might impact on the welfare of large
numbers of people. The proposed research will develop translational methodology that cuts across disciplines and can be used to improve modeling and forecasting in a variety of settings. Suggested areas of application include those with which the PI is most familiar because of his ongoing collaborations (quantitative psychology, marketing, and patient oriented medical investigation) but there is clear potential for the research to have an impact on other areas as well. For example, finite mixture distributions models, one of the specific research themes, are used in applied settings as diverse as human genetics and the monitoring of worldwide nuclear testing to tell explosions apart from earthquakes. The project also has a clear educational focus, both in terms of training of the graduate students who will assist the PI in the research activities and in terms of alerting the broader research community to the need for sound and modern modeling strategies.

Repeated measurements taken on the same person are usually highly correlated and also influenced by changes in that individual's mental or physical state over time. Accurate conclusions about why a person's performance changes over time, as well as accurate hypotheses about how tasks are performed, require non-Gaussian time series models that can separate changes in performance due to changes in task conditions from changes in a person's mental or physical state. At present, techniques available for the analysis of human performance data are limited. In particular, models for repeated response time measurements usually fail to consider that the measurements are correlated and that overall speed may naturally fluctuate over time, even when all other task conditions remain the same. This project will address this problem by developing realistic models for response time series that provide a basis for simultaneously explaining the generating mechanism as well as describing trends due to changes in a person's state over time. An important component of this project will be the development of new computational methods for effectively fitting these statistical models as well as evaluating the model fits.

Response time measurements are important because how well people perform tasks is often measured, at least in part, by how quickly they can accomplish those tasks. In many situations, tasks are repetitive, requiring decisions and actions that recur many times within a fixed period of time. Such tasks, while commonly performed in psychological laboratories, are also used in a number of real-world settings such as assembly line work, during standardized testing, and in athletics. This project will result not only in better techniques of analysis for these kinds of measurements, but also in the development of more accurate and realistic models of how people perform repetitive tasks. A diverse cross-section of students (psychological and statistical) will be mentored in methods that both bridge and strengthen their two disciplines. All data collected and general-purpose software developed under this award will be made available (via the World Wide Web) to the research community.

This research project will develop new statistical models to facilitate the analysis of human performance data. The improved techniques will reduce the need for ad hoc data processing and increase the amount of data available for analysis. The factors that influence human performance usually extend beyond those identified as important by a researcher's restricted theoretical framework. A person's level of education, for example, may well influence performance of a simple task for which a theory of perception concerns only levels of illumination and spatial location. As a result, it often is difficult to determine why particular people fail to perform tasks as expected. Researchers rely on ad hoc strategies to identify and remove from a data set people who perform poorly or who seem unmotivated. Such strategies generally have little theoretical justification and thus have the potential to degrade the information available in the data and to introduce bias in the conclusions drawn from the data. The models developed in this research will help ensure the accuracy of conclusions drawn from experiments on human performance. These models will be of interest to researchers across a range of disciplines that care about human performance data and also may be applied to other types of data in medicine, engineering, and finance. New software will be developed and made available to other researchers. The project will contribute to the training of both undergraduate and graduate students in Psychology and Statistics and help further connections between those disciplines.

Learning about the processes that determine how well people perform tasks in different circumstances requires at least two things: first, a theoretical framework consisting of models that can predict how the human cognitive system responds to and interacts with the environment, and, second, accurate and robust statistical techniques that can be used to analyze data within the context of these models. The investigators will develop hierarchical Bayesian models that incorporate stimulus-independent response strategies to minimize the need for data pre-processing. The models will separate task appropriate (stimulus-dependent) from task inappropriate ( stimulus-independent) responding in such a way that (i) no data need to be removed, and (ii) task performance changes over time can be examined within a coherent theoretical framework. The researchers will collect new data from experiments that will provoke people to move from task-appropriate to task-inappropriate performance strategies over time. This will enable the investigators to evaluate their theories of human performance and the techniques they will develop to analyze the data.

This research project will develop a cohesive set of Bayesian data analysis tools for non-generative models. A generative statistical model provides a complete technical description of a phenomenon. Such a model is detailed enough that one can generate a full data set from it, including observations at the individual level as well as the population level. In essence, the generative model provides access to an artificial world. These models are prevalent in the physical sciences where there is the possibility of having a full and complete technical description of the world. In contrast, many applied fields make use of non-generative models. This type of model is based on theory that describes the key features of a phenomenon while leaving minor features unspecified. These models have proven their worth in a variety of fields, including econometrics, the main area of application considered in this project. The project will focus on Bayesian methods that have traditionally relied on generative statistical models. The Bayesian paradigm provides a rich environment for the development of data-analytic techniques for identification of deficiencies in models and remediation of the effects of shortcomings of the data. The project will develop a full suite of analogous Bayesian inferences and diagnostics for non-generative models and will implement them in substantive empirical contexts from econometrics. The project involves international and multidisciplinary collaboration between the three investigators with direct opportunities for their students. Often working with students from underrepresented groups in STEM fields, including women and minorities, the investigators will engage in cross-mentoring to deepen the students' views of both statistics and econometrics and to provide them with insight into the strengths and weaknesses of the educational systems in the US and Australia.

This research project will take techniques developed for data analysis with generative models and adapt them for use with non-generative models specified by a set of (generalized) moment constraints. Within this context, empirical likelihood enables a form of likelihood-driven inference based on an empirically derived likelihood function satisfying the moment constraints. As many existing data analysis techniques are likelihood based, the project will consider empirical likelihood versions of these models. The eventual goal is to improve moment-based model data analysis by expanding the toolkit for the moment-based modeler. The researchers will: 1) Develop a suite of case influence diagnostics within the Bayesian empirical likelihood context and investigate the theoretical and empirical properties of these diagnostics; 2) Develop Bayesian empirical likelihood methods for hypothesis testing, model comparison, and model averaging, with attention to formulation of the null hypothesis; and 3) Apply the tools developed under points 1 and 2 to a range of econometric applications; for example, to the modeling of asset prices and short-term interest rates.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.