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Statistical Sciences Seminar Series Abstracts for 2007
Optimal Buffer Size for a Stochastic Processing Network with a Drift
Arka Ghosh
Iowa State University
We consider a one dimensional stochastic control problem that arises in queueing network applications where the controller can choose the arrival and/or service rates and the buffer size b is finite (i.e. customers are rejected if the queue-length exceeds b). This model is similar to the model in Ata-Harrison-Shepp (Annals of Applied Probability, 2005) where the buffer size is kept fixed. We take a long run average cost (``ergodic cost") criterion, which has components corresponding to the cost for arrival/service rate control, holding cost for the customers in the queue as well as a penalty for rejecting customers when the buffer is full. For this cost criterion, we obtain the optimal drift rate (i.e. optimal rates for arrivals and services) as well as the optimal buffer size b*.
Our approach involves analyzing a family (indexed by the buffer size b) of ordinary differential equations, where the b-th equation is the Hamilton-Jacobi-Bellman (HJB) equation for the drift control problem in stochastic processing networks with fixed buffer size b. We demonstrate a simple approach to construct solution for this HJB equation (and thus the optimal drift rate) for each buffer size b. This analysis simplifies some of the proofs in Ata-Harrison-Shepp. We make use of some specific characteristics of the family of solutions to choose the optimal buffer size b*.
Scalable Ad Hoc Broadcast
Rudolf Riedi
Rice University
With the prevalence of digital information, the dependence of today's industrialized societies on networking infrastructure is growing to a critical degree. It aggravates the digital divide and renders economies and societies vulnerable to disasters and attacks. The Safari project aims at providing connectivity and basic network services in a self-organizing fashion, using available infrastructure when and where it exists.
This talk addresses key issues of relevance to scalability in Ad Hoc Networking: A close look at the Broadcast Storm and the Dynamics of Flooding using Poisson-based Connectivity Models, and a study of fundamental limitations of broadcast capacity. If time permits an optimal, low maintenance broadcast scheme via a coloring backbone will be proposed.
Degradation Modeling and Reliability Inference
Vijay Nair
University of Michigan
Degradation data are a very rich source of reliability information and offer many
advantages over the analysis of time-to-failure data. We will first describe concepts
related to degradation rates and contrast them with the familiar notions that arise in time-to-failure and time-between failure data. We will then consider a class of models for
degradation data based on non-homogeneous Gaussian processes and describe various
types of inference for the degradation function and reliability distribution. These models
can accommodate a variety of degradation rates and shapes. The inverse Gaussian
distribution plays a central role, similar to the exponential distribution with hazard rates.
This is joint work with Xiao Wang.
Some Applications and Misapplications of Probability and Statistics
Anthony Hayter
University of Denver
Various applications of statistical and probabilistic techniques are
discussed concerning wheelchair design, multiplicity issues, flow rates
of the Nile river, hot rolling mill processes in the steel industry,
variability concepts, residential property taxes, detective stories,
recursive integration methodologies, erosion around the foundations of
bridge piers, and airborne contaminants. These examples illustrate the
substantial advantages that accrue from a clear understanding of the
concepts of probability and statistics, together with the pitfalls that
can arise from their misuse.
Using Open Source to Build and Analyze Global Systems
Rajan Gupta
LANL, T-8
I will provide a couple of examples on how tools like Google Earth, Wiki, Web 2.0 are allowing us to engage the public in open source to build sophisticated and reliable databases. Once we develop statistical and inferencing tools to validate and collate the data, we can have real time display, assessment and analysis of global systems. Long term goal is to integrate hard information of physical infrastructure with social, political, economic drivers for realistic understanding of these systems.
Using Field Data to Assess the Risk of Product Failures
William Meeker
Iowa State University / LANL, CCS-6 Affiliate
Unanticipated failure modes are the primary cause of serious product reliability failures. After such a failure mode is discovered for a product that is already in the field, an immediate question that management needs to answer is “what is the financial risk of failures of product already in the field?” Risks can involve costs ranging to excessive warranty returns to loss of human life. Limited field failure data, often with complications, perhaps supplemented by engineering information, are generally used to make the needed assessment. In this talk, I will discuss some well-known and some not-so-well-known examples of unanticipated failure modes and the risks involved. I will then outline some details of the statistical methods of life data analysis that were used to assess risk for one particular product.
Calibrating a Computer Code in the Presence of Systematic Discrepancy
Presenter: Jason Loeppky
University of British Columbia-Okanagan
Authors: Jason Loeppky, (UBC-O), William Welch (UBC), and Brian Williams (LANL)
Computer models to simulate physical phenomena are now widely available in engineering and science. Before relying on a computer model, a natural first step is often to compare its output with physical or field data, to assess whether the computer model reliabily represents the real world. Field data, when available, can also be used to calibrate unknown paramters in the computer model. Calibration can be particularly problematic in the presence of systematic discrepancies between the computer model and field observations. In this talk we present results on a simulation study that is designed to assess how well the calibration parameter has been estimated, and the conditions under which calibration is possible. By simulating both computer model data, and physical observations from a Gaussian process the uncertainty due to using the incorrect model does not arise. This allows us a more accurate picture of the problems that can arise when attempting to calibrate the model in the presence of systematic discrepancy.
Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors
Zhiguang (Peter) Qian
University of Wisconsin-Madison
Modeling experiments with qualitative and quantitative factors is an important and challenging issue in computer modeling. In this talk, I will discuss a framework for building Gaussian process models with these two types of factors. The key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors. An iterative estimation procedure is developed for the proposed models. Modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions. The proposed method is illustrated with an example involving a known function and a real example for modeling data center thermal distribution.
The Minimal Belief Principle: A New Method for Parametric Inference
Chuanhai Liu and Jianchun Zhang
Purdue University
The classical belief in distributional invariance of pivotal variables for statistical inference is often stronger than necessary. A "minimal belief" (MB)-based method is considered for parametric inference. The MB principle serves as a general guidance rather than a precisely defined mathematical term. It may take different mathematical forms for sampling models of different data structures. The proposed method can be viewed as an extension of Fisher's fiducial argument as well as a variant of the Dempster-Shafer (DS) theory. The MB posteriors for general single- parameter distributions and certain multiparameter distributions are obtained in closed form. While being developed, especially for multiparameter models, the method is illustrated with a variety of examples, including the simple test of significance, the Behren-Fisher problem, the multinomial model, and a normal model involving a large number of unknown location parameters. It is also shown that Markov chain Monte Carlo methods, which have made the Bayesian methodology computationally attractive, can be developed for MB-based analysis.
Comparing Competing Resource Allocation Strategies Using Entropy in the Reliability of Complex Systems
Jessica Chapman
Iowa State University
A primary goal in complex system reliability is to estimate the reliability of the full system. The most direct method of obtaining this estimate would be to perform many full system tests. However, in practice, the number of these tests that are actually performed can be rather small because they are either too expensive or impossible to perform. In many cases, however, it may be possible to obtain data from other less direct, but still informative, sources to aid in the estimation of the full system reliability. Quality assurance data, maintenance data or measurements from common components in related systems are all examples of these other sources of data. Our interest in the problem involves resource allocation. Data from the different sources have different inherent value and collection costs. It is important, and challenging, to allocate additional resources among these different data sources so as to obtain the most information about the reliability of the full system.
This talk will focus on the resource allocation problem in the context of a k-component series system which has pass/fail data, not dependent upon time, available at component and system levels. Entropy is commonly used in Bayesian experimental design and is proposed as a new metric for quantifying information gain in this resource allocation problem. The current approach to evaluating a given metric is computationally intensive and involves repeated runs of an MCMC program. A potentially time-saving approach requiring only a single MCMC run will be presented. An experiment designed to explore the behavior of entropy under various system conditions will also be discussed.
The Marginalization Paradox and the Formal Bayes' Law
Tim Wallstrom
LANL, T-13: Complex Systems
The marginalization paradox (MP) involves an inconsistency in improper Bayesian inference, i.e., Bayesian inference using priors that integrate to infinity, rather than one. Two Bayesians use two different methods to compute the same marginal posterior, and get inconsistent results. The MP was discovered in 1972, and has been a mystery ever since.
In this talk, I show that the MP can be resolved by changing the sense in which an improper inference is required to be a limit of proper inferences. In fact, the inconsistency disappears when we use the probability limits of Mervyn Stone, rather than the pointwise limits of Harold Jeffreys. Probability limits, unlike pointwise limits, have a solid conceptual basis, and have previously been shown to resolve many of the other paradoxes of improper inference.
I will discuss the resolution of the MP, and the consequences for Bayesian inference of using probability limits to define improper inferences. One important consequence is that Bayes' law is no longer valid when the prior is improper.
Fully Non-parametric Bayesian Ensemble Modelling
Hugh Chipman, Edward George, and Robert McCulloch
(University of Chicago)
In "BART: Bayesian Additive Regression Tree" (2006), Chipman, George, and McCulloch developed a fully Bayesian approach to the model: y = f(x) + e where the errors are iid normal. In the spirit of "ensembel models'' the unknown function $f$ was modelled as the sum of many simple tree models. The contribution of each individual tree was kept small through the use of a strong regularization prior. The BART methodology was shown to be very competive in terms of out-of-sample prediction. Because the MCMC draws gives a natural quantification of the uncertainty and the BART model may be imbedded in a large hierarchical model (see Zhan, Shih, and Mueller (2006, for example).
However, the BART approach is not fully flexible because the simple iid normal error specification is used. In this paper we relax this assumption by modelling the errors with a Dirichlet process. Various specification and prior choices are explored. The costs as well as the benefits of the more flexible approach are illustrated.
Robert McCulloch obtained his Ph.D. in 1985 from the University of Minnesota Department of Statistics. He is currently the Sigmund E. Edelstone Professor of Chicago Graduate School of Business. His research in Bayesian statistics, with application to data mining, finance, and marketing.
Joint Munitions Program Munitions Stockpile Reliability Assessment Project (U)
Alyson Wilson, LANL, CCS-6
This talk will be classified (unclassified abstract) and is part of the Joint Munitions Program Seminar Series
The goal of the Munitions Stockpile Reliability Assessment project is to provide a suite of methods and tools for assessing stockpile reliability as part of a cost-benefit framework for assessing surveillance data collection activities. This project leverages DoD conventional munitions functional and surveillance data to develop new tools and methods for DOE Enhanced and Core Surveillance programs. Tools and methods created as part of this project are also transitioned back to our DoD partners with the goal of providing them with the ability to predict munitions performance more cost efficiently and with better uncertainty quantification. In this talk I will discuss the broad framework for these analyses with examples from DOE and DoD systems.
Dr. Alyson Wilson is a project leader for the Systems MTE of the Enhanced Surveillance Campaign and a technical staff member in the Statistical Sciences Group (CCS-6) at Los Alamos National Laboratory. Prior to her move to Los Alamos, Dr. Wilson was a senior operations research systems analyst working in support of the U.S. Army Operational Evaluation Command, Air Defense Artillery Evaluation Directorate. She received her Ph.D. in Statistics from the Institute of Statistics and Decision Sciences at Duke University.
Lessons about Likelihood Functions from Nuclear Physics
Ken Hanson
LANL, T-16: Nuclear Physics
Least-squares data analysis is based on the assumption that the normal (Gaussian) distribution appropriately characterizes the likelihood, that is, the conditional probability of each measurement d, given a measured quantity y, p(d | y). On the other hand, there is ample evidence in nuclear physics of significant disagreements among measurements, which are inconsistent with the normal distribution, given their stated uncertainties. In this study the histories of 99 measurements of the lifetimes of five elementary particles are examined to determine what can be inferred about the distribution of their values relative to their stated uncertainties. Taken as a whole, the variations in the data are somewhat larger than their quoted uncertainties would indicate. These data strongly support using a Student t distribution for the likelihood function instead of a normal. The most probable value for the order of the t distribution is 2.6 +/- 0.9. It is shown that analyses based on long-tailed t-distribution likelihoods gracefully cope with outlying data.
The Adaptive COSSO for Multiple Predictor Function Estimation
Curt Storlie
University of New Mexico
We propose a new regularization method for simultaneous model fitting and variable selection in nonparametric regression models in the framework of smoothing spline ANOVA. This method is an improvement on the COSSO which penalizes the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. Here we introduce an adaptive weight to be used in the COSSO penalty which allows for more flexibility to estimate important functional components while giving heavier penalty to unimportant functional components. We call this method the Adaptive COSSO (ACOSSO). Theoretical properties including consistency and the rate of convergence of the ACOSSO are established. Furthermore, we show that ACOSSO possesses a nonparametric analog of the oracle property. This is the first result of this type for any nonparametric regression estimator. The utility of ACOSSO is illustrated on several examples including its use as a meta model for a complex computer model.
A Critique of Standard Cosmology
Jayant Narlikar
Inter-University Centre for Astronomy and Astrophysics
This talk will discuss the strengths and weaknesses of the standard big bang model. The former will include the prediction of light nuclear abundances and the relic radiation background. The latter will dwell upon the very speculative nature of the various assumptions that have gone to make up the present 'concordance' or 'precision' cosmology. It will be argued that the field of theoretical cosmology should be kept open for alternative models.
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Past Seminars
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