2016 INFORMS Annual Meeting Program

MD40

INFORMS Nashville – 2016

MD39 207A-MCC Markov Lecture Sponsored: Applied Probability Sponsored Session Chair: David Goldberg, GA Institute of Technology, Atlanta, GA 30332-0205, dgoldberg9@isye.gatech.edu Co-Chair: Rouba Ibrahim, University College London, rouba.ibrahim@ucl.ac.uk 1 - Piecewise Deterministic Markov Processes For Monte Carlo Traditional MCMC approaches for sampling complex distributions are almost all based on the Metropolis-Hastings framework, which, although versatile, restrict algorithms to be reversible, discrete time, and to require target density evaluation at each iteration. All of these features can sometimes be significant disadvantages. To overcome these difficulties, new algorithms are being developed which are non-reversible and continuous in time, for example the Zigzag, Bouncy Particle sampler, and the SCALE and CIS algorithms. The first two of these are pure MCMC algorithms whereas the latter two involve combination with sequential Monte Carlo methods. They all share the property that they can be couched in terms of Piecewise Deterministic Markov processes. The presentation will also touch on the impressive theoretical and empirical properties of these methods, including the super-efficiency properties of the zigzag algorithm, the unbiased subsampling properties of the SCALE approach and the stability of the CIS importance sampling approach, and is based on joint work with Joris Bierkens, Paul Fearnhead, Adam Johansen, and Krys Latuszynski. 2 - Adaptive MCMC For Everyone Jeffrey Rosenthal, University of Toronto, Toronto, ON, Canada, rosenthal, jeff@math.toronto.edu In this discussion, we shall briefly discuss the theory behind “adaptive” Markov chain Monte Carlo (MCMC), which automatically modify the algorithm while it runs in an effort to improve its performance “on the fly”. Adaptation can greatly improve convergence, but it can also destroy the ergodicity properties necessary for the algorithm to be valid. We shall present some examples and theorems concerning the ergodicity and efficiency of adaptive MCMC, with an aim towards making it more widely applicable in broader contexts 3 - Optimal Scaling Of MCMC Algorithms Natesh Pillai, Harvard University, Cambridge, MA, United States, nateshspillai@gmail.com In this discussion, we will give a brief overview of optimal scaling of MCMC algorithms. Optimal scaling offers a new perspective for studying the efficiency of MCMC algorithms in high dimensions. The key idea is to study the properties of the proposal distribution as a function of the dimension. This point of view gives us new insights on the behavior of the algorithm, such as precise estimates of the number of steps required to explore the target measure as a function of the dimension of the state space. After reviewing the original results, we will mention some recent progress as well. MD40 207B-MCC Theoretical Development in Estimation Invited: Data Envelopment Analysis Invited Session Chair: Ole Olesen, Southern Denmark University, Campusvej 55, Odense, 5230, Denmark, ole@sam.sdu.dk 1 - An Improved Afriat-Diewert-Parkan Nonparametric Production Function Estimator Ole Olesen, Southern Denmark University, ole@sam.sdu.dk, John Ruggiero Nonparametric regression estimators with shape constraints have recently been extended based on the Afriat inequalities. Overfitting of the ADP estimator suggests that estimators based on a weighted average of restricted estimators may provide an equally unbiased estimator but an estimator with lower variance. Both an Average Random k-Hinge estimator, a Jackknife Model Average (JMA) or a slightly modified JMA are considered. Small sample properties of the estimators are presented Gareth Roberts, University of Warwick, Coventry, United Kingdom, Gareth.O.Roberts@warwick.ac.uk

3 - Price Competition Based On Relative Prices Or Subsidies Awi Federgruen, Columbia University, New York, NY, United States, af7@gsb.columbia.edu, Lijian Lu We consider price competition models for oligopolistic markets in which the consumer reacts to relative rather than absolute prices. The relative price is defined as the difference between the absolute price and a reference value., either a third party subsidy or a prospect theoretical reference price. Application areas We review five different application areas. We then characterize the equilibrium behavior under general reference value scheme , assuming the consumer choice model is of the general MultiNomial Logit type. We also derive comparison results for the price equilibria that arise under alternative Subsidy schemes. These have important applications for the design of subsidy schemes. 4 - Risk-aware Demand Management Of Aggregators Participating In Energy Programs With Utilities Ana Radovanovic, Google, anaradovanovic@google.com We present a methodology for modeling and optimally managing the demand of an aggregator with deferrable (flexible) loads (e.g., electric vehicles and HVACs) under uncertainty. We propose a unified framework for treating different types of flexible loads, that captures uncertainties in their parameters, and environmental conditions they are exposed to. Our optimization formulation minimizes the total expected cost, whose goal is to optimally balance two terms: user discomfort cost (regret), and cost paid to the utility. We propose a cost-efficient procedure for risk estimation, and provide guidelines for its consideration in cost-effective program selection. Chair: Zhimin Xi, University of Michigan-Dearborn, 4901 Evergreen Road, 2240 HPEC, Dearborn, MI, 48128, United States, zxi@umich.edu 1 - Estimation Of Field Reliability Based On Aggregate Lifetime Data Piao Chen, National University of Singapore, Singapore, Singapore, cp@u.nus.edu Because of the exponential distribution assumption, many reliability databases recorded data in an aggregate way. The data format is different from traditional lifetime data and the statistical inference is challenging. In this study, we model the aggregate data by gamma distribution and inverse Gaussian (IG) distribution. Statistical inference methods are proposed. 2 - ALT With Exponentially Changing Stress Durations Under Cost Constraint David Han, University of Texas at San Antonio, Management Science & Statistics, College of Business, San Antonio, TX, 78249-0632, United States, david.han@utsa.edu When designing ALT, several variables such as the allocation proportions and stress durations must be determined carefully because of constrained resources. This talk discusses the optimal decision variables based on the popular optimality criteria under the constraint that the total cost does not exceed a pre-specified budget. A general scale family of distributions is considered to accommodate different lifetime models for flexible modeling with exponentially decreasing stress durations. 3 - Fault Localization Of A Series System When Tests Are Imperfect Tonguc Unluyurt, Sabanci University, Orhanli Tuzla, Istanbul, 34956, Turkey, tonguc@sabanciuniv.edu, Zahed Shahmoradi We consider a failed series system. The goal is to find the component that caused the failure with the minimum expected cost. In order to do this, we conduct costly tests and we know the probability that a certain component is the reason of the failure. The complicating factor is the fact that tests are imperfect and this is described by type I and type II error probabilities. In addition to the testing costs, we also consider misclassification costs. In order to decrease the total cost we develop a model that allows repetition of the tests in a certain way. We compute the expected cost of such a solution and we demonstrate the potential savings resulting from repetition of tests. 4 - Model Uncertainty Approximation Using A Copula-based Approach For Reliability Based Design Optimization Zhimin Xi, University of Michigan-Dearborn, 4901 Evergreen Road, 2240 HPEC, Dearborn, MI, 48128, United States, zxi@umich.edu Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting reliability constraints. Model uncertainty, i.e., the uncertainty of model bias indicating the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty approximation in a product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias modeling approach is proposed and results are demonstrated by two vehicle design problems. MD38 206A-MCC Reliability Contributed Session

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