C. Shane Reese

Integrated Analysis of Computer and Physical Experiments

Scientific investigations frequently involve data from computer experiment(s) as well as related physical experimental data on the same factors and related response variable(s). There may also be one or more expert opinions regarding the response of interest. Traditional statistical approaches consider each of these datasets separately with corresponding separate analyses and fitted statistical models. A compelling argument can be made that better, more precise statistical models can be obtained if the combined data are analyzed simultaneously using a hierarchical Bayesian integrated modeling approach. However, such an integrated approach must recognize important differences, such as possible biases, in these experiments and expert opinions. We illustrate our proposed integrated methodology by using it to model the thermodynamic operation point of a top-spray fluidized bed microencapsulation processing unit. Such units are used in the food industry to tune the effect of functional ingredients and additives. An important thermodynamic response variable of interest, Y, is the steady-state outlet air temperature. In addition to a set of physical experimental observations involving six factors used to predictY, similar results from three different computer models are also available. The integrated data from the physical experiment and the three computer models are used to fit an appropriate response surface (regression) model for predicting Y.

Bridging Different Eras in Sports

Abstract This article addresses the problem of comparing abilities of players from different eras in professional sports. We study National Hockey League players, professional golfers, and Major League Baseball players from the perspectives of home run hitting and hitting for average. Within each sport, the careers of the players overlap to some extent. This network of overlaps, or bridges, is used to compare players whose careers took place in different eras. The goal is not to judge players relative to their contemporaries, but rather to compare all players directly. Hence the model that we use is a statistical time machine. We use additive models to estimate the innate ability of players, the effects of aging on performance, and the relative difficulty of each year within a sport. We measure each of these effects separated from the others. We use hierarchical models to model the distribution of players and specify separate distributions for each decade, thus allowing the “talent pool” within each sport...

Advances in Data Combination, Analysis and Collection for System Reliability Assessment

The systems that statisticians are asked to assess, such as nuclear weapons, infrastructure networks, supercomputer codes and munitions, have become increasingly complex. It is often costly to conduct full system tests. As such, we present a review of methodology that has been proposed for addressing system reliability with limited full system testing. The first approaches presented in this paper are concerned with the combination of multiple sources of information to assess the reliability of a single component. The second general set of methodology addresses the combination of multiple levels of data to determine system reliability. We then present developments for complex systems beyond traditional series/parallel representations through the use of Bayesian networks and flowgraph models. We also include methodological contributions to resource allocation considerations for system relability assessment. We illustrate each method with applications primarily encountered at Los Alamos National Laboratory.

A Bayesian Model for Integrating Multiple Sources of Lifetime Information

We present a Bayesian model for assessing the reliability of multicomponent systems. Novel features of this model are the natural manner in which lifetime data collected at either the component, subsystem, or system level are integrated with prior information at any level. The model allows pooling of information between similar components, the incorporation of expert opinion, and straightforward handling of censored data. The methodology is illustrated with two examples.

Estimation of Fetal Growth and Gestation in Bowhead Whales

We address estimating fetal growth and gestation for bowhead whales of the Bering, Chukchi, and Beaufort seas stock. This population is subject to a subsistence hunt by Eskimo whale hunters, which is monitored via a quota system established by the International Whaling Commission. Quota determination is assisted by biological information, such as fetal growth and gestation, which is the basis of a population dynamics model used to estimate the annual replacement yield of the stock. We developed a Bayesian hierarchical nonlinear model for fetal growth with computation carried out via Markov chain Monte Carlo techniques. Our model allows for unique conception and parturition dates and provides predictive distributions for gestation length and conception dates. These results are used to propose estimates of geographic locations for conception and parturition. A sensitivity analysis indicated caution when specifying some hyperparameters related to growth rate, conception dates, and parturition dates.

Hierarchical Models for Permutations: Analysis of Auto Racing Results

The popularity of the sport of auto racing is increasing rapidly, but its fans remain less interested in statistics than the fans of other sports. In this article, we propose a new class of models for permutations that closely resembles the behavior of auto racing results. We pose the model in a Bayesian hierarchical framework, which permits hierarchical specification and fully hierarchical estimation of interaction terms. We demonstrate the methodology using several rich datasets that consist of repeated rankings for a collection of drivers. Our models can potentially identify individuals racing in “minor league” divisions who have higher potential for competitive performance at higher levels. We also present evidence that one of the sports more controversial figures, Jeff Gordon, is a statistically dominant figure.

Incorporating Time-Dependent source Profiles Using the Dirichlet Distribution in Multivariate Receptor Models.

Multivariate receptor modeling is used to estimate profiles and contributions of pollution sources from concentrations of pollutants such as particulate matter in the air. The majority of previous approaches to multivariate receptor modeling assume pollution source profiles are constant through time. In an effort to relax this assumption, this article uses the Dirichlet distribution in a dynamic linear receptor model for pollution source profiles. The receptor model developed herein is evaluated using simulated datasets and then applied to a physical dataset of chemical species concentrations measured at the U.S. Environmental Protection Agency’s St. Louis–Midwest supersite. Supplemental materials to this articles are available online.

Parameter tuning for a multi-fidelity dynamical model of the magnetosphere

Geomagnetic storms play a critical role in space weather physics with the potential for far reaching economic impacts including power grid outages, air traffic rerouting, satellite damage and GPS disruption. The LFM-MIX is a state-of-the-art coupled magnetospheric-ionospheric model capable of simulating geomagnetic storms. Imbedded in this model are physical equations for turning the magnetohydrodynamic state parameters into energy and flux of electrons entering the ionosphere, involving a set of input parameters. The exact values of these input parameters in the model are unknown, and we seek to quantify the uncertainty about these parameters when model output is compared to observations. The model is available at different fidelities: a lower fidelity which is faster to run, and a higher fidelity but more computationally intense version. Model output and observational data are large spatiotemporal systems; the traditional design and analysis of computer experiments is unable to cope with such large data sets that involve multiple fidelities of model output. We develop an approach to this inverse problem for large spatiotemporal data sets that incorporates two different versions of the physical model. After an initial design, we propose a sequential design based on expected improvement. For the LFM-MIX, the additional run suggested by expected improvement diminishes posterior uncertainty by ruling out a posterior mode and shrinking the width of the posterior distribution. We also illustrate our approach using the Lorenz `96 system of equations for a simplified atmosphere, using known input parameters. For the Lorenz `96 system, after performing sequential runs based on expected improvement, the posterior mode converges to the true value and the posterior variability is reduced.

Diversification and Focus: A Bayesian Application of the Resource-Based View

We propose a new application of the resource-based view (RBV) that is more consistent with Penrose’s (1959) original framework. We use that framework to study the relationship between diversification and refocusing strategies and economic performance. We propose that the RBV may be enhanced by the explicit recognition of Penrose’s two classes of resources, administrative and productive resources. This distinction suggests a focus on the administrative decisions of managers, including the multiple decisions associated with diversification and refocusing strategies, which lead to economic performance. Second, we argue that RBV theory is a theory about extraordinary performers or outliers, not averages. Therefore, the statistical methods used in applying the theory should account for the difference between individual firms, rather than relying on means across firms, which statistically neutralize firm differences. We introduce a novel Bayesian Hierarchical method to examine actions taken by new CEOs and the resulting effects on economic performance over time. The unique feature of this Bayesian method is it allows us to make meaningful probability statements about the diversification and refocusing strategies of individual firms.

Assessing system reliability by combining multilevel data from different test modalities.

Abstract In this paper, we show how to estimate the reliability of an entire system for a specified period of time when the available data may be at different levels of the system and come from different test modalities and consequently vary in fidelity. We propose a hierarchical statistical model for binary data which allows all available data to be used while faithfully accounting for these differences. This allows one to provide a better estimate of system reliability under use conditions even when some of test modalities are harsher than use conditions. We take a Bayesian approach and show how it can be implemented in WinBUGS. The proposed methodology is illustrated with an example.