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A double Metropolis-Hastings sampler for spatial models with intractable normalizing constants

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2010年第9期80卷 1007-1022页

作者： Liang, Faming Texas A&M Univ Dept Stat College Stn TX 77843 USA

The problem of simulating from distributions with intractable normalizing constants has received much attention in recent literature. In this article, we propose an asymptotic algorithm, the so-called double Metropolis-Hastings (MH) sampler, for tackling this problem. Unlike other auxiliary variable algorithms, the double MH sampler removes the need for exact sampling, the auxiliary variables being generated using MH kernels, and thus can be applied to a wide range of problems for which exact sampling is not available. For the problems for which exact sampling is available, it can typically produce the same accurate results as the exchange algorithm, but using much less CPU time. The new method is illustrated by various spatial models.

关键词： autologistic model autonormal model auxiliary variable MCMC algorithm exchange algorithm Metropolis-Hastings algorithm

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Scarf Oiks

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 1281-1288页

作者： Edmonds, Jack Gaubert, Stéphane Gurvich, Vladimir INRIA and École Polytechnique France RUTCOR Rutgers University Piscataway NJ 08854 640 Bartholomew Road United States

We formulate the famous Scarf Lemma in terms of oiks. This lemma has two fundamental applications in game and graph theory. In 1967, Scarf derived from it core-solvability of balanced cooperative games. Recently, it was shown that kernel-solvability of perfect graphs also results from this *** show that Scarf's combinatorially defined oiks are in fact realized by polytopes, and also that Scarf's algorithm for proving the Scarf Lemma is an instance of the Lemke-Howson algorithm for finding an equilibrium of a bimatrix ***, we give a sequence of two equal d-dimensional Scarf oiks on 2. d vertices such that the pivoting path of the algorithm grows exponentially with d. © 2010 Elsevier B.V.

关键词： Balanced games Euler complex (oik) exchange algorithm Kernel Kernel-solvability Perfect graph Pivot Room Scarf Lemma Wall

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Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions

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JOURNAL OF FINANCIAL ECONOMETRICS 2010年第4期8卷 450-480页

作者： Stramer, Osnat Bognar, Matthew Schneider, Paul Univ Iowa Dept Stat & Actuarial Sci Iowa City IA 52242 USA Warwick Business Sch Warwick England

This article proposes a new Bayesian Markov chain Monte Carlo (MCMC) methodology for estimation of a wide class of multidimensional jump-diffusion models. Our approach is based on the closed-form (CF) likelihood approximations of Ait-Sahalia (2002, 2008). The CF likelihood approximation does not integrate to 1;it is very close to 1 when in the center of the distribution but can differ markedly from 1 when far in the tails. We propose an MCMC algorithm that addresses the problems that arise when the CF approximation is applied in a Bayesian context. The efficacy of our approach is demonstrated in a simulation study of the Cox-Ingersoll-Ross and Heston models and is applied to two well-known datasets.

关键词： C11 C15 G63 Bayesian inference closed-form likelihood exchange algorithm jump-diffusion process

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Computer Aided Construction of Efficient Multi-level Supersaturated Designs

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2010年第2期4卷 221-231页

作者： Gupta, V. K. Singh, Poonam Kole, Basudev Parsad, Rajender IASRI Lib Ave New Delhi 110012 India Univ Delhi Dept Stat Delhi India

Motivated by the computer search algorithms for constructing two-level supersaturated designs by Heavlin and Finnegan (1993), Li and Wu (1997), Nguyen (1996), Lejeune (2003) and Gupta, Parsad, Kole and Bhar (2008), this paper develops an algorithm to generate multi-level supersaturated designs. Popular E (f(NOD)) and E (chi(2)) criterion have been used as a measure of non-orthogonality for the designs generated. The algorithm also ensures that no two columns in the designs generated are fully aliased. A catalogue of 120 optimal supersaturated designs for different number of factors m, design runs n, with 5 <= n <= 16 runs, and different number of factor levels q, with 3 <= q <= 6, has been prepared. All the designs generated are f(NOD)-optimal;some designs are chi(2)-optimal

关键词： exchange algorithm Efficiency criteria Supersaturated design

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Sperner Oiks

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 1273-1280页

作者： Edmonds, Jack Gaubert, Stéphane Gurvich, Vladimir INRIA and École Polytechnique France RUTCOR Rutgers University Piscataway NJ 08854 640 Bartholomew Road United States

The idea of "Lemke pivoting in a family of oiks (Euler complexes)" generalizes, and abstracts to pure combinatorics, the Lemke-Howson exchange algorithm for finding a Nash equilibrium in bimatrix games, as well as the classical algorithm for finding the properly colored room in Sperner's Lemma. Given a "room-partitioning", this algorithm finds another (distinct) room-partitioning by traversing the exchange graph. In this paper we show that each family of k oiks O={O1, ... ,Ok} can be reduced to a pair of oiks O'={O1+ ... +Ok,O0} (one of which, O0, is a Sperner oik) such that the exchange graphs for O and O' are isomorphic. Numerous applications of Sperner's Lemma in combinatorial topology are well known. © 2010 Elsevier B.V.

关键词： Brouwer Theorem Euler complex (oik) exchange algorithm KKM-Theorem Lemke-Howson algorithm Manifold Pivot Room Sperner Lemma Wall

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Euler Complexes (Oiks)

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 1289-1293页

作者： Edmonds, Jack Canada and Paris

We present a class of instances of the existence of a second object of a specified type, in fact, of an even number of objects of a specified type, which generalizes the existence of an equilibrium for bimatrix games. The proof is an abstract generalization of the Lemke-Howson algorithm for finding an equilibrium of a bimatrix *** of this note, with various examples, were presented at a Dagstuhl conference in 2007, the Dubrovnik ECCO XXI conference in 2008, the Paris TGGT conference in 2008, and the Bonn conference, "Recent trends in Combinatorial Optimization", proceedings: Springer, 2009. The version here is meant to be updated convenience for the session on Oiks, ISCO, 2010. © 2010.

关键词： 05C85 68R10 68W40 91A05 Binary matroid Euler binary matroid Euler complex Euler graph exchange algorithm Lemke-Howson algorithm Matching algorithm Matroid partition algorithm Nash equilibrium Room family Room partition Simplicial pseudo-manifold

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On finding another room-partitioning of the vertices

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 1257-1264页

作者： Edmonds, Jack Sanità, Laura Equipe Combinatoire Optimisation Université Pierre et Marie Curie Paris France Institute of Mathematics Ecole Polytechnique Fèdèrale de Lausanne Lausanne Switzerland

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning of T is a subset R of the rooms such that each vertex of T is in exactly one room in *** prove that if T has a room-partitioning R, then there is another room-partitioning of T which is different from R. The proof is a simple algorithm which walks from room to room, which however we show to be exponential by constructing a sequence of (planar) instances, where the algorithm walks from room to room an exponential number of times relative to the number of rooms in the *** unify the above theorem with Nash's theorem stating that a 2-person game has an equilibrium, by proving a combinatorially simple common generalization. © 2010 Elsevier B.V.

关键词： 2-person games exchange algorithm Room-partitioning

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Multi-modal vibration control using a synchronized switch based on a displacement switching threshold

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SMART MATERIALS AND STRUCTURES 2009年第3期18卷 035016:1-035016:8页

作者： Ji, Hongli Qiu, Jinhao Zhu, Kongjun Chen, Yuansheng Badel, Adrien Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn Aeronaut Sci Key Lab Smart Mat & Struct Nanjing 210016 Peoples R China Savoie Univ Lab Syst & Mat Mechatron Polytech Savoie F-74944 Annecy Le Vieux France

A new semi-active method for multi-mode vibration control using the nonlinear synchronized switch damping (SSD) approach based on a displacement switching threshold is proposed in this paper. Several extensions of the SSD approach, including SSDI (SSD on inductance), SSDV (SSD on a voltage source), enhanced SSDV, and adaptive SSDV, have been developed to improve the control of the single-mode vibration, but the weakness of the SSD approach for multi-modal vibration control has not been solved. In all these extensions of the SSD approach, the switch is controlled by the same algorithm, that is, it reverses the voltage of the piezoelectric element at all extrema of displacement. This switching algorithm is effective in single-mode control, but it leads to over-frequent switching in multi-mode control. In the method proposed in this study, an improved switching algorithm based on a displacement threshold, which prevents the switch in the shunt circuit from over-frequent on-and-off actions and accordingly increases the converted energy to improve the control performance, is proposed. The switching algorithm is applied to an SSDI system and used in the vibration damping of a beam with two excited modes. Compared to the classical SSDI approach, the control performance of the first mode is improved from 3.7 to 18.2 dB, but that of the second mode is slightly worse, having changed from 3.46 to 2.6.

关键词： VOLTAGE SOURCES ABSORBER absorbers voltage source SYNCHRONIZING SWITCHES shunt circuit exchange algorithm vibration control Threshold control performance Dislocated Workers Social Security Disability Insurance absorption of shock

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Model-robust supersaturated and partially supersaturated designs

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2009年第1期139卷 45-53页

作者： Jones, Bradley A. Li, William Nachtsheim, Christopher J. Ye, Kenny Q. Univ Minnesota Carlson Sch Management Operat & Management Sci Dept S Minneapolis MN 55455 USA SAS Inst Cary NC 27513 USA Albert Einstein Coll Med Dept Epidemiol & Populat Hlth Bronx NY 10461 USA

Supersaturated designs are an increasingly popular tool for screening factors in the presence of effect sparsity. The advantage of this class of designs over resolution III factorial designs or Plackett-Burman designs is that n, the number of runs, can be substantially smaller than the number of factors. m. A limitation associated with most supersaturated designs produced thus far is that the capability of these designs for estimating g active effects has not been discussed. In addition to exploring this capability, we develop a new class of model-robust supersaturated designs that, for a given n and m. maximizes the number g of active effects that can be estimated simultaneously. The capabilities of model-robust supersaturated designs for model discrimination are assessed using a model-discrimination criterion, the subspace angle. Finally, we introduce the class of partially supersaturated designs, intended for use when we require a specific subset of m, core factors to be estimable, and the sparsity of effects principle applies to the remaining (m - m(1)) factors. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Estimation capacity exchange algorithm Model-robust design Optimal design Partially supersaturated design Supersaturated design

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Bayesian D-optimal supersaturated designs

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2008年第1期138卷 86-92页

作者： Jones, Bradley Lin, Dennis K. J. Nachtsheim, Christopher J. SAS Inst Cary NC 27513 USA Penn State Univ Dept Supply Chain & Informat Syst University Pk PA 16802 USA Univ Minnesota Carlson Sch Management Minneapolis MN 55455 USA

We introduce a new class of supersaturated designs using Bayesian D-optimality. The designs generated using this approach can have arbitrary sample sizes, can have any number of blocks of any size, and can incorporate categorical factors with more than two levels. In side by side diagnostic comparisons based on the E(s(2)) criterion for two-level experiments having even sample size, our designs either match or out-perform the best designs published to date. The generality of the method is illustrated with quality improvement experiment with 15 runs and 20 factors in 3 blocks. (c) 2007 Elsevier B.V. All rights reserved.

关键词： blocking exchange algorithm model robust designs ridge regression screening designs

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