Department of Statistics

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A Note on the General Likelihood Measure of Overlap
Smith, Eric P. (Ecological Society of America, 1984)
Attrition Models of the Ardennes Campaign
Fricker, Ronald D. Jr. (1998)
Department of Statistics Newsletter, Winter 2001
(Virginia Tech, 2001)
This is the annual newsletter of Virginia Tech’s Department of Statistics.
Department of Statistics Newsletter, Winter 2002
(Virginia Tech, 2002)
This is the annual newsletter of Virginia Tech’s Department of Statistics.
Bayesian QTL mapping using skewed Student-tdistributions
von Rohr, Peter; Hoeschele, Ina (2002-01-15)
In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.
A Model to Predict the Impact of Specification Changes on Chloride-Induced Corrosion Service Life of Virginia Bridge Decks
Trevor J. Kirkpatrick; Richard E. Weyers; Anderson-Cook, Christine M.; Michael M. Sprinkel; Michael C. Brown (Virginia Center for Transportation Innovation and Research, 2002-10)
A model to determine the time to first repair and subsequent rehabilitation of concrete bridge decks exposed to chloride deicer salts that recognizes and incorporates the statistical nature of factors affecting the corrosion process is developed. The model expands on an existing deterministic model by using statistical computing techniques, including resampling techniques such as the parametric and simple bootstrap. Emphasis was placed on the diffusion portion of the diffusion-cracking model, but advances can be readily included for the time for corrosion deterioration after corrosion initiation. Data collected from ten bridge decks built in Virginia between 1981 and 1994 were used to model the surface chloride concentration, apparent diffusion coefficient, and clear cover depth. Several ranges of the chloride corrosion initiation concentration, as determined from the available literature, were investigated. The time to first repair and subsequent rehabilitation predicted by the stochastic model is shorter than the time to first repair and subsequent rehabilitation predicted by the deterministic model. The stochastic model is believed to more accurately reflect the true nature of bridge deck deterioration because it takes into account the fact that data for each of the parameters affecting chloride diffusion and corrosion initiation are not necessarily normally distributed. The model was validated by comparison of projected service lives of bridge decks built from 1981 to 1994 derived from the model to historical service life data for 129 bridge decks built in Virginia between 1968 and 1972. The time to rehabilitation predicted for the set of bridge decks built between 1981 and 1994 by the stochastic model was approximately 13 years longer than the normalized time to rehabilitation projected for the bridge decks built between 1968 and 1972 using historical data. The time to first repair and rehabilitation predicted by the probabilistic method more closely matches that of historical data than the time to first repair and rehabilitation predicted by the average value solution. The additional service life expected for the set of bridges built between 1981 and 1994 over those constructed from 1968 to 1972 can be attributed to the decrease in w/c ratio from 0.47 to 0.45 and slight increase in as-built cover depth from approximately 50 mm (2 in.) to 63.5 to 76 mm (2.5 to 3.0 in.).
Department of Statistics Newsletter, Fall 2004
(Virginia Tech, 2004)
This is the annual newsletter of Virginia Tech’s Department of Statistics.
Construction Concepts for Continuum Regression
Spitzner, Dan J. (Virginia Tech, 2004-08-28)
Approaches for meaningful regressor construction in the linear prediction problem are investigated in a framework similar to partial least squares and continuum regression, but weighted to allow for intelligent specification of an evaluative scheme. A cross-validatory continuum regression procedure is proposed, and shown to compare well with ordinary continuum regression in empirical demonstrations. Similar procedures are formulated from model-based constructive criteria, but are shown to be severely limited in their potential to enhance predictive performance. By paying careful attention to the interpretability of the proposed methods, the paper addresses a long-standing criticism that the current methodology relies on arbitrary mechanisms.
On the Distribution of Hotelling's T² Statistic Based on the Successive Differences Covariance Matrix Estimator
Williams, James D.; Woodall, William H.; Birch, Jeffrey B.; Sullivan, Joe H. (Virginia Tech, 2004-09-30)
In the historical (or retrospective or Phase I) multivariate data analysis, the choice of the estimator for the variance-covariance matrix is crucial to successfully detecting the presence of special causes of variation. For the case of individual multivariate observations, the choice is compounded by the lack of rational subgroups of observations with the same distribution. Other research has shown that the use of the sample covariance matrix, with all of the individual observations pooled, impairs the detection of a sustained step shift in the mean vector. For example, research has shown that, with the use of the sample covariance matrix, the probability of a signal actually decreases below the false alarm probability with a sustained step shift near the middle of the data and that the signal probability decreases with the size of the shift. An alternative estimator, based on the successive differences of the individual observations, leads to an increasing signal probability as the size of the step shift increases and has been recommended for use in Phase I analysis. However, the exact distribution for the resulting T² chart statistics has not been determined when the successive differences estimator is used. Three approximate distributions have been proposed in the literature. In this paper we demonstrate several useful properties of the T² statistics based on the successive differences estimator and give a more accu- rate approximate distribution for calculating the upper control limit for individual observations in a Phase I analysis.
Evaluating And Interpreting Interactions
Hinkelmann, Klaus H. (Virginia Tech, 2004-12-13)
The notion of interaction plays an important − and sometimes frightening − role in the analysis and interpretation of results from observational and experimental studies. In general, results are much easier to explain and to implement if interaction effects are not present. It is for this reason that they are often assumed to be negligible. This may, however, lead to erroneous conclusions and poor actions. One reason why interactions are sometimes feared is because of limited understanding of what the word “interaction” actually means, in a practical sense and,in particular, in a statistical sense. As far as the latter is concerned, simply stating that interaction is significant is generally not sufficient. Subsequent interpretation of that finding is needed, and that brings us back to the definition and meaning of interaction within the context of the experimental setting. In the following sections we shall define and discuss various types of variables that affect the response and the types of interactions among them. These notions will be illustrated for one particular experiment to which we shall return throughout our discussion. To help us in the interpretation of interactions we take a closer look at the definitions of two-factor and three-factor interactions in terms of simple effects. This is followed by a discussion of the nature of interactions and the role they play in the context of the experiment, from the statistical point of view and with regard to the interpretation of the results. After a general overview of how to dissect interactions we return to our example and perform a detailed analysis and interpretation of the data using SASr (SAS Institute, 2000), in particular PROC GLM and some of its options, such as SLICE. We mention also different methods for the analysis when interaction is actually present. We conclude the analytical part with a discussion of a useful graphical method when no error term is available for testing for interactions. Finally, we summarize the results with some recommendation reminding the reader that in all of this the experimental design is of fundamental importance.
A Bayesian Hierarchical Approach to Dual Response Surface Modeling
Chen, Younan; Ye, Keying (Virginia Tech, 2005)
In modern quality engineering, dual response surface methodology is a powerful tool to monitor an industrial process by using both the mean and the standard deviation of the measurements as the responses. The least squares method in regression is often used to estimate the coefficients in the mean and standard deviation models, and various decision criteria are proposed by researchers to find the optimal conditions. Based on the inherent hierarchical structure of the dual response problems, we propose a hierarchical Bayesian approach to model dual response surfaces. Such an approach is compared with two frequentist least squares methods by using two real data sets and simulated data.
Department of Statistics Newsletter, Fall 2005
(Virginia Tech, 2005)
This is the annual newsletter of Virginia Tech’s Department of Statistics.
High Breakdown Estimation Methods for Phase I Multivariate Control Charts
Jensen, Willis A.; Birch, Jeffrey B.; Woodall, William H. (Virginia Tech, 2005)
The goal of Phase I monitoring of multivariate data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. However, they are difficult to implement in practice due to the extensive computation required to obtain the estimates. Based on previous studies, it is not clear which of these two estimation methods is best for control chart applications. The comprehensive simulation study here gives guidance for when to use which estimator, and control limits are provided. High breakdown estimation methods such as MCD and MVE, can be applied to a wide variety of multivariate quality control data.
Robust Parameter Design: A Semi-Parametric Approach
Pickle, Stephanie M.; Robinson, Timothy J.; Birch, Jeffrey B.; Anderson-Cook, Christine M. (Virginia Tech, 2005)
Parameter design or robust parameter design (RPD) is an engineering methodology intended as a cost-effective approach for improving the quality of products and processes. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic. An essential component of robust parameter design involves the assumption of well estimated models for the process mean and variance. Traditionally, the modeling of the mean and variance has been done parametrically. It is often the case, particularly when modeling the variance, that nonparametric techniques are more appropriate due to the nature of the curvature in the underlying function. Most response surface experiments involve sparse data. In sparse data situations with unusual curvature in the underlying function, nonparametric techniques often result in estimates with problematic variation whereas their parametric counterparts may result in estimates with problematic bias. We propose the use of semi-parametric modeling within the robust design setting, combining parametric and nonparametric functions to improve the quality of both mean and variance model estimation. The proposed method will be illustrated with an example and simulations.
Cost Penalized Estimation and Prediction Evaluation for Split-Plot Designs
Liang, Li; Anderson-Cook, Christine M.; Robinson, Timothy J. (Virginia Tech, 2005-02-02)
The use of response surface methods generally begins with a process or system involving a response y that depends on a set of k controllable input variables (factors) x₁, x₂,…,xk. To assess the effects of these factors on the response, an experiment is conducted in which the levels of the factors are varied and changes in the response are noted. The size of the experimental design (number of distinct level combinations of the factors as well as number of runs) depends on the complexity of the model the user wishes to fit. Limited resources due to time and/or cost constraints are inherent to most experiments, and hence, the user typically approaches experimentation with a desire to minimize the number of experimental trials while still being able to adequately estimate the underlying model.
Speculations Concerning the First Ultraintelligent Machine
Good, Irving John (Virginia Tech, 2005-03-05)
The survival of man depends on the early construction of an ultraintelligent machine. In order to design an ultraintelligent machine we need to understand more about the human brain or human thought or both. In the following pages an attempt is made to take more of the magic out of the brain by means of a "subassembly" theory, which is a modification of Hebb's famous speculative cell-assembly theory. My belief is that the first ultraintelligent machine is most likely to incorporate vast artificial neural circuitry, and that its behavior will be partly explicable in terms of the subassembly theory. Later machines will all be designed by ultra-intelligent machines, and who am I to guess what principles they will devise? But probably Man will construct the deus ex machina in his own image.
Protecting Against Biological Terrorism: Statistical Issues in Electronic Biosurveillance
Fricker, Ronald D. Jr.; Rolka, H. R. (2006)
Executive Summary Statistics Department 2005-2006
(Department of Statistics, 2006)
Profile Monitoring via Nonlinear Mixed Models
Jensen, Willis A.; Birch, Jeffrey B. (Virginia Tech, 2006)
Profile monitoring is a relatively new technique in quality control best used where the process data follows a profile (or curve) at each time period. Little work has been done on the monitoring on nonlinear profiles. Previous work has assumed that the measurements within a profile are uncorrelated. To relax this restriction we propose the use of nonlinear mixed models to monitor the nonlinear profiles in order to account for the correlation structure. We evaluate the effectiveness of fitting separate nonlinear regression models to each profile in Phase I control chart applications for data with uncorrelated errors and no random effects. For data with random effects, we compare the effectiveness of charts based on a separate nonlinear regression approach versus those based on a nonlinear mixed model approach. Our proposed approach uses the separate nonlinear regression model fits to obtain a nonlinear mixed model fit. The nonlinear mixed model approach results in charts with good abilities to detect changes in Phase I data and has a simple to calculate control limit.
A Semiparametric Approach to Dual Modeling
Robinson, Timothy J.; Birch, Jeffrey B.; Starnes, B. Alden (Virginia Tech, 2006)
In typical normal theory regression, the assumption of homogeneity of variances is often not appropriate. When heteroscedasticity exists, instead of treating the variances as a nuisance and transforming away the heterogeneity, the structure of the variances may be of interest and it is desirable to model the variances. Modeling both the mean and variance is commonly referred to as dual modeling. In parametric dual modeling, estimation of the mean and variance parameters are interrelated. When one or both of the models (the mean or variance model) are misspecified, parametric dual modeling can lead to faulty inferences. An alternative to parametric dual modeling is nonparametric dual modeling. However, nonparametric techniques often result in estimates that are characterized by high variability and ignore important knowledge that the user may have regarding the process. We develop a dual modeling approach [Dual Model Robust Regression (DMRR)], which is robust to user misspecification of the mean and/or variance models. Numerical and asymptotic results illustrate the advantages of DMRR over several other dual model procedures.

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