SPES Short Courses at the 2009 Joint Statistical Meetings

Submitted by Tena Katsaounis, SPES Education Chair

SPES is sponsoring the following four short courses at the Joint Statistical Meetings 2009. Please check the upcoming JSM2009 online program for courses dates and sites.

See you at JSM09!

Tena Katsaounis
SPES Continuing Education Chair

Monte Carlo and Bayesian Computation with R
Jim Albert and Maria Rizzo.

Maria Rizzo and Jim Albert are professors in the Department of Mathematics and Statistics at Bowling Green State University.  Dr. Rizzo regularly teaches a doctoral-level course in statistical computing and has recently published a text on statistical computing using R.  Dr. Albert has regularly taught a course in Bayesian inference and has written several texts on Bayesian modeling and computation. Dr. Albert has previously taught short courses at JSM on ordinal data modeling (with Val Johnson) and on the use of sports in teaching statistics.

This course is intended for statisticians who are interested in using the R system to design Monte Carlo experiments to assess the properties of statistical procedures.  Also, the course will be helpful for statisticians who wish to learn about the use of R as an environment for Bayesian computations.  It is helpful if the participant has some familiarity with the R system and Bayesian thinking.

The participants will learn about how R can be used to simulate random variates and design a Monte Carlo experiment to learn about a property of a statistical procedure.  The participant will learn how to implement simulation-based inferential procedures on R such as the bootstrap and permutation test.  In addition, the participant will learn how to write a R function to define a posterior density in Bayesian inference, and how to use different R tools to simulate from the posterior distribution and summarize the simulated sample to perform inferences.

Abstract:

This course describes the use of the statistical system R in Monte Carlo experiments, simulation-based inference, and Bayesian computation.  R tools are described for generating random variables, computing criteria of statistical procedures, and replicating the procedure to compute quantities such as mean squared error and probability of coverage.  R commands for implementing simulation-based procedures such as bootstrap and permutation tests are outlined.  The use of R in Bayesian computation is described, including the programming of the posterior distribution and the use of different R tools to summarize the posterior.  Special focus will be on the application of Markov chain Monte Carlo algorithms and diagnostic methods to assess convergence of the algorithms.

Outline of Topics:

  1. Review of Classical and Bayesian Statistical Inference
  2. Methods for Generating Random Variables
  3. Design of Monte Carlo Experiments in R
  4. Simulation-based Inferential Methods in R including Bootstrapping and Permutation Tests
  5. Introduction to Bayesian Computation
  6. Setting up a Bayesian Problem in R
  7. Markov Chain Monte Carlo Methods
  8. Illustrations of Bayesian Computation with R

Methods for Designing & Analyzing Mixture Experiments
John A. Cornell and Greg F. Piepel.

Prof. John Cornell is Professor Emeritus with the Department of Statistics and Agricultural Experiment Station at the University of Florida.  He has worked as a consultant to industry and in the agricultural sciences in the area of mixture experiments for the past 41 years.  He has been an active researcher during this time, with over 150 publications in the fields of experimental design, mixture experiments, and other areas.  He is the author of the text Experiments with Mixtures (3rd edition, 2002) and is also a co-author of Response Surfaces, Designs and Analyses with A.I. Khuri (2nd edition, 1996).  Professor Cornell a Fellow of the ASA and the ASQ.  He is a past editor of the Journal of Quality Technology.

Dr. Greg Piepel is a Laboratory Fellow in the Statistics and Sensor Analytics Group at Pacific Northwest National Laboratory operated by Battelle Memorial Institute.  He works as an applied statistician on multi-disciplinary research projects in the physical and engineering sciences.  He has developed and applied mixture experiment techniques to a wide variety of problems (e.g., glass, ceramics, cement, stainless steel, aluminum production, drugs) over the past 29 years.  He has over 120 publications and technical reports in the areas of mixture experiments, experimental design, and others. He is the developer since 1989 of MIXSOFT, software toolkit for the design and analysis of mixture experiments.  Dr. Piepel is a Fellow of ASA, has held several positions with ASA-SPES and ASQ

The course will be valuable to several groups:  (1) statisticians who work in fields where mixture experiments occur or who would like to know more about the subject, (2) instructors who teach design of experiments and data analysis courses and would like to include more mixture experiment material in their courses, and (3) formulators, engineers, chemists, or scientists who work with mixtures and have some background in experimental design and data analysis.

Attendees will:

  1. come away with an understanding of what mixture experiments are and how they differ from the standard, independent factor-type experiments,
  2. learn how to design mixture experiments for both simplex- and irregular-shaped regions,
  3. be familiar with the various classes of mixture model forms, know how to fit the models to data, and learn how to interpret the blending properties of the components from the fitted models.

The following textbook is recommended but not necessary for the course.  John A. Cornell (2002), Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data, 3rd Edition, John Wiley & Sons, Inc., New York.  Publisher contact is Fred Filler, Marketing Manager, who can be contacted at ffiller@wiley.com or (201) 748-6078).  Copies of the book will be available to course attendees at the special discounted cost of 20% off the retail price.

Abstract

Mixture experiments involve varying the component proportions of a product and observing the changes in the product's properties.  The component proportions cannot be varied independently because they must sum to 1.0 for each run in the experiment.  Mixture experiments are useful in many product development areas, including foods, drinks, drugs, plastics, alloys, ceramics, glass, gasoline, fertilizers, and others.  The course will provide an overview of approaches and methods used in designing mixture experiments and analyzing the resulting data.  Designs for simplex-shaped and irregular-shaped regions (the latter resulting from constraints on the component proportions) will be covered.  Various types of mixture models for fitting to mixture data will be discussed, as will graphical techniques for interpreting component effects.  Including process variables and/or a total amount variable in mixture experiments will be covered.  Graphical and analytic methods for developing mixtures with optimum properties will also be discussed.  Many examples from the presenters’ experiences will be used to illustrate the topics.  The course is designed for statisticians and non-statisticians wanting to know about statistical methods for designing mixture experiments and analyzing the resulting data.  Prerequisites are an understanding of basic statistics concepts and some previous exposure to experimental design and regression.

Course outline:

  1. INTRODUCTION
    1. What are mixture experiments and how do they differ from standard (e.g., factorial) experiments?
    2. Types (and examples) of mixture experiments
  2. DESIGNS AND MODELS FOR EXPLORING THE ENTIRE SIMPLEX FACTOR SPACE
    1. Simplex-Lattice Designs
    2. Scheffe's Canonical Polynomial Models
    3. A Three-Component Yarn Example
    4. The Correct Analysis of Variance Table
    5. The Simplex-Centroid Design and Associated Polynomial Model
    6. Axial Designs
    7. Reparametrizing Scheffé Polynomial Models to Contain a Constant Term
  3. DESIGNS WHEN THERE ARE CONSTRAINTS ON THE COMPONENT PROPORTIONS
    1. Lower Bounds on Some or All of the Component Proportions
    2. Introducing L-Pseudocomponents: An Example
    3. Lower and Upper Bounds on the Component Proportions
    4. Extreme Vertices and Centroids
    5. Design Strategies for Fitting First- and Second-Degree Models
    6. Multicomponent Constraints
    7. Examples of Designs for Constrained Mixture Regions
  4. THE ANALYSIS OF MIXTURE DATA
    1. Test Statistics for Testing the Usefulness of the Terms in the Scheffé Polynomials
    2. Measuring the Effects of Individual Components
    3. Contour Plots and Plotting the Response Trace
    4. Other Mixture Model Forms
      1. Models with Inverse Terms
      2. Models Homogeneous of Degree One
      3. Polynomials with Ratio Terms
      4. Slack-Variable Models
  5. INCLUDING PROCESS VARIABLES AND/OR A TOTAL AMOUNT VARIABLE
    1. Designs Formed by Combining Lattice Designs with Factorial Arrangements
    2. A Fish Patty Experiment Example
    3. Restricting the Randomization of the Experimental Trials
    4. Computer-Aided Fractional Designs
    5. Mixture-Amount Experiments: An Example
  6. SELECTING MIXTURES WITH OPTIMUM PROPERTIES
    1. Contour Plots
    2. Grid Searches
    3. Constrained Non-Linear Optimization
    4. Desirability Functions
    5. Sequential Experimental Optimization
  7. SUMMARY OF MIXTURE DESIGNS AND MODEL FORMS

Note: Examples taken from the consulting experiences of both presenters will be used extensively throughout the course to illustrate the topics.

Tolerance Intervals: Theory, Applications and Computation
Thomas Mathew and K. Krishnamoorthy.

Thomas Mathew is a Professor, at the Department of Mathematics and Statistics, University of Maryland, Baltimore County Campus. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He is a winner of ASA's 2005 Youden Award for Inter-laboratory Testing. He is Presidential Research Professor at the University of Maryland, Baltimore County Campus. He is also a co-author of the book (jointly with A. I. Khuri and B. K. Sinha) Statistical Tests for Mixed Linear Models, published by John Wiley in 1998.

K. Krishnamoorthy holds the Philip and Jean Piccione Endowed Professor position at the University of Louisiana at Lafayette. He is the author of the book Statistical Distributions with Applications and StatCalcTM Software, published by Chapman & Hall/CRC, 2006.

The presenters have contributed significantly to the areas of mixed model inference, tolerance intervals and regions, and multivariate analysis. Their current research interests are focused on the tolerance interval problem, with applications in environmental monitoring and industrial hygiene. The authors have contributed to the development of tolerance factors for random effects models and for multivariate normal models. Their work, which appeared in Technometrics (1999), appears to be the first attempt to provide a satisfactory tolerance factor for a multivariate normal population. Their later papers in Technometrics (2004, 2007) provide solutions to the tolerance interval problem for the one-way random model and for the gamma distribution. In addition to Technometrics, the authors' research work has appeared in several leading journals in statistics, including the Journal of the American Statistical Association, Journal of the Royal Statistical Society, Annals of Statistics, and Journal of Statistical Planning and Inference. Their continued interest in the tolerance interval problem has culminated in the book Statistical Tolerance Regions: Theory, Applications and Computation, to be published by John Wiley (2009).

The course is aimed at statisticians in industry, graduate students, and applied statisticians, with an interest in regression, analysis of variance and quality control. A major goal is to expose the attendees to the established as well as the latest methodologies for the derivation and computation of tolerance limits. In the context of random effects models and multivariate normal models, satisfactory tolerance limits have been developed only very recently, i.e., during the 2000's. Attendees will become familiar with these developments, including the computational procedures. They will also learn simple and easy to use algorithms for computing tolerance limits for models for which table values of tolerance factors are not available. The attendees will gain insight regarding the role of tolerance intervals in applied work a role that has not been widely recognized. For those who want to undertake a detailed study of tolerance intervals for other models and problems (not covered in the course), the course will provide the necessary insight and background.

Abstract:

Tolerance intervals have numerous industrial applications, especially in the physical, engineering and environmental sciences. A tolerance interval (or region) contains a specified proportion of a population, with a certain confidence. The problem has been investigated in various parametric settings: univariate normal models, random effects models, univariate regression models, multivariate normal models etc., and also in nonparametric settings. Even though work on tolerance intervals dates back to the 1940's, satisfactory solutions and computational algorithms were obtained for many models only very recently. The purpose of the short course is to present the state of the art on the tolerance interval problem, explain computational procedures, and describe various applications in the physical, engineering and environmental sciences, quality control, and industrial hygiene. In the short course, the problem will be addressed under the above parametric settings, a nonparametric set up, and also under a few other continuous distributions (gamma, exponential and Weibull). Computational issues will be addressed and illustrated with practical examples using real data. Algorithms will be provided so that it can be coded in machine languages such as Fortran, C or SAS. The prerequisites for the course are a basic knowledge of ANOVA and mixed models, regression, and multivariate analysis.

Course outline:

The course will consist of seven lectures based on the authors' forthcoming book, Statistical Tolerance Regions: Theory, Applications and Computation, John Wiley (2009). The topics to be covered in each lecture are as follows:

Lecture 1: Introduction. The concept of a tolerance interval and motivating examples. The tolerance interval problem for the univariate normal distribution, for the one-way random model and for the linear regression model. The concept of simultaneous tolerance intervals  for a linear regression model. Tolerance regions for multivariate normal populations. Nonparametric tolerance intervals. The concept of generalized confidence intervals.

Lecture 2: One-sided and two-sided tolerance limits for univariate normal populations. Approximations for the tolerance factor. Tolerance limits that control both tails. Tolerance limits for comparing two normal populations. Inference concerning survival probability. Sample size calculation. Examples and applications.

Lecture 3: The one-way random model with balanced and unbalanced data. Difficulties associated with unbalanced data. Some examples and applications. Computation of one-sided and two-sided tolerance limits. Approximations for the tolerance factor. Computational algorithms. Numerical results and examples.

Lecture 4: The linear regression model. Computation of tolerance limits. Approximations for the tolerance factor and comparisons of the approximations. Computation of a simultaneous tolerance interval. An approximation for the simultaneous tolerance factor. The calibration problem. Examples and applications.

Lecture 5: Tolerance limits for the gamma, exponential and Weibull distributions. Accurate normal approximations to derive gamma tolerance limits. Exact tolerance limits for the two-parameter exponential distribution. One-sided tolerance limits for the Weibull distribution. Interval estimation of survival probability. Inference concerning tress-strength reliability. Illustrative examples and applications.

Lecture 6: Nonparametric Tolerance Intervals based on order statistics. One-sided tolerance limits and exceedance probabilities. Two-sided tolerance intervals. Confidence intervals for population quantiles. Sample size calculation. Examples and applications.

Lecture 7: The multivariate normal distribution. Tolerance regions for a multivariate normal population. Some approximations for the tolerance factor and numerical comparisons. Tolerance regions for the multivariate linear regression model. Practical recommendations and examples.

Experiences and Pitfalls in Reliability Data Analysis and Test Planning
William Q. Meeker

William Q. Meeker is a Professor of Statistics and Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He is a Fellow of the American Statistical Association (ASA) and the American Society for Quality (ASQ). He is a past Editor of Technometrics and is currently an Associate Editor for Life Time Data Analysis. He is co-author of the books Statistical Methods for Reliability Data with Luis Escobar (1998), and Statistical Intervals: A Guide for Practitioners with Gerald Hahn (1991), six book chapters, and of numerous publications in the engineering and statistical literature.  He has won the ASQ Youden prize four times and the ASQ Wilcoxon Prize three times. He was recognized by the ASA with their Best Practical Application Award in 2001 and by the ASQ Statistics Division’s with their W.G. Hunter Award in 2003. In 2007 he was awarded the ASQ Shewhart medal. Meeker has won two awards for outstanding teaching at Iowa State University and Outstanding Presentation awards from the ASA Section of Physical and Engineering Sciences. He has done research and consulted extensively on problems in reliability data analysis, reliability test planning, accelerated testing, nondestructive evaluation, and statistical computing.

The material in this course will be of interest and accessible to individuals ranging from engineers having had only one or two courses of statistics in their education/training through individuals with advanced degrees in statistics. The course will be of interest to those working in manufacturing industries, as well as those involved in the collection and analysis of biological survival data.

After completing this course, participants should understand how to

Abstract:

Reliability assurance processes in manufacturing industries require data-driven information for making product-design decisions. Life tests, accelerated life tests, and accelerated degradation tests are commonly used to collect reliability data. Data from products in the field provide another important source of useful reliability information. These reliability studies typically yield data that are censored and/or truncated, require the use of less familiar distributions like the Weibull, the lognormal, and the gamma, and call for inferences that involve extrapolation.

This course will present and discuss the analyses of many different life data analysis applications in the area of product reliability and materials evaluation. The analyses illustrate the use of a mix of proven traditional techniques, enhanced and brought up to date with modern computer-based methodology. Methods used in the analyses include nonparametric estimation, probability plotting, maximum likelihood estimation of parametric models, analysis of data with multiple failure modes, acceleration models, Bayesian methods, degradation analysis, and the analysis of recurrence data from repairable systems. 

Using a series of real examples from reliability applications, this course will focus on graphical presentation of reliability data, statistical modeling, and interpretation of results. The prerequisite is a course in applied statistics covering material through simple linear regression.

Course outline:

Morning session: Analysis of Field Data

Afternoon Session: Accelerated Life Testing

Textbook:

Meeker, W. Q. and Escobar, L. A. (1998), Statistical Methods for Reliability Data, John Wiley and Sons, New York.