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Record 1 of 5: FN ISI Export Format VR 1.0 PT J AU Gottardo, R Raftery, AE AF Gottardo, Raphael Raftery, Adrian E. TI Markov Chain Monte Carlo With Mixtures of Mutually Singular Distributions SO JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS LA English DT Article DE Gibbs sampler; Metropolis-Hastings algorithm; Mixture distribution; Rao-Blackwellization; Reversible jump; Singular measures ID EXPLORING POSTERIOR DISTRIBUTIONS; BAYESIAN VARIABLE SELECTION; REVERSIBLE JUMP; LINEAR-REGRESSION; SAMPLING METHODS; GENE-EXPRESSION; UNKNOWN NUMBER; MODEL; IDENTIFICATION; COMPONENTS AB Markov chain Monte Carlo (MCMC) methods for Bayesian computation are mostly used when the dominating measure is the Lebesgue measure, the counting measure, or a product of these. Many Bayesian problems give rise to distributions that are not dominated by the Lebesgue measure or the counting measure alone. In this article we introduce a simple framework for using MCMC algorithms in Bayesian computation with mixtures of mutually singular distributions. The idea is to find a common dominating measure that allows the use of traditional Metropolis-Hastings algorithms. In particular, using our formulation, the Gibbs sampler can be used whenever the full conditionals are available. We compare Our formulation with the reversible jump approach and show that the two are closely related. We give results for three examples, involving testing a normal mean, variable selection in regression, and hypothesis testing for differential gene expression under multiple conditions. This allows us to compare the three methods considered: Metropolis-Hastings with mutually singular distributions, Gibbs sampler with mutually Singular distributions, and reversible jump. In our examples, we found the Gibbs sampler to be more precise and to need considerably less computer time than the other methods. In addition, the full conditionals used in the Gibbs sampler call be used to further improve the estimates of the model posterior probabilities via Rao-Blackwellization, at no extra cost. C1 [Gottardo, Raphael] Univ British Columbia, Dept Stat, Vancouver, BC V6T 1Z2, Canada. [Raftery, Adrian E.] Univ Washington, Dept Stat, Seattle, WA 98195 USA. RP Gottardo, R, Univ British Columbia, Dept Stat, 333-6356 Agr Rd, Vancouver, BC V6T 1Z2, Canada. EM raph@stat.ubc.ca raftery@stat.washington.edu FU NIH [8 R01 EB002137 02, 1 R01 HD054511 01 A1] FX The authors thank Julian Besag, Charlie Geyer, Peter Hoff, Matthew Stephens and Jeffrey Rosenthal for helpful discussions, Luke Bormi for proofreading the manuscript, and three anonymous referees and the editor for suggestions that improved an earlier version of the article. This research was supported by NIH Grants 8 R01 EB002137 02 and 1 R01 HD054511 01 A1. NR 45 TC 0 PU AMER STATISTICAL ASSOC PI ALEXANDRIA PA 1429 DUKE ST, ALEXANDRIA, VA 22314 USA SN 1061-8600 J9 J COMPUT GRAPH STAT JI J. Comput. Graph. Stat. PD DEC PY 2008 VL 17 IS 4 BP 949 EP 975 DI 10.1198/106186008X386102 PG 27 SC Statistics & Probability GA 497MN UT ISI:000270063700011 ER EF Record 2 of 5: FN ISI Export Format VR 1.0 PT J AU Hoff, PD AF Hoff, Peter D. TI Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data SO JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS LA English DT Article DE Bayesian inference; Eigenvalue decomposition; Markov chain Monte Carlo; Random matrix; Social network; Stiefel manifold AB Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that includes linear and quadratic terms in the log-density, and arises as a posterior distribution in latent factor models for multivariate and relational data. This article describes rejection and Gibbs sampling algorithms for sampling from this family of distributions, and illustrates their use in the analysis of a protein-protein interaction network. Supplemental materials, including code and data to generate all of the numerical results in this article, are available online. C1 [Hoff, Peter D.] Univ Washington, Dept Stat, Seattle, WA 98195 USA. [Hoff, Peter D.] Univ Washington, Dept Biostat, Seattle, WA 98195 USA. [Hoff, Peter D.] Univ Washington, Ctr Stat & Social Sci, Seattle, WA 98195 USA. RP Hoff, PD, Univ Washington, Dept Stat, Seattle, WA 98195 USA. EM hoff@stat.washington.edu FU NSF [SES-0631531] FX The author thanks the editor, associate editor, and two referees for their suggestions on improving the readability and consistency of this article. This work was partially funded by NSF Grant SES-0631531 NR 15 TC 0 PU AMER STATISTICAL ASSOC PI ALEXANDRIA PA 1429 DUKE ST, ALEXANDRIA, VA 22314 USA SN 1061-8600 J9 J COMPUT GRAPH STAT JI J. Comput. Graph. Stat. PD JUN PY 2009 VL 18 IS 2 BP 438 EP 456 DI 10.1198/jcgs.2009.07177 PG 19 SC Statistics & Probability GA 497MO UT ISI:000270063800011 ER EF Record 3 of 5: FN ISI Export Format VR 1.0 PT J AU Ferreira, DD Kenig, CE Salo, M Uhlmann, G AF Ferreira, David Dos Santos Kenig, Carlos E. Salo, Mikko Uhlmann, Gunther TI Limiting Carleman weights and anisotropic inverse problems SO INVENTIONES MATHEMATICAE LA English DT Article ID BOUNDARY-VALUE PROBLEM; CONDUCTIVITY PROBLEM; GLOBAL UNIQUENESS; 2 DIMENSIONS; NEUMANN MAP; CAUCHY DATA; MANIFOLDS; EQUATION; PLANE AB In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig et al. (Ann. Math. 165: 567-591, 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic ray transform. Earlier results in dimension n >= 3 were restricted to real-analytic metrics. C1 [Ferreira, David Dos Santos] Univ Paris 13, LAGA, F-93430 Villetaneuse, France. [Kenig, Carlos E.] Univ Chicago, Dept Math, Chicago, IL 60637 USA. [Salo, Mikko] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland. [Uhlmann, Gunther] Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Ferreira, DD, Univ Paris 13, LAGA, F-93430 Villetaneuse, France. EM ddsf@math.univ-paris13.fr cek@math.uchicago.edu mikko.salo@helsinki.fi gunther@math.washington.edu NR 37 TC 0 PU SPRINGER PI NEW YORK PA 233 SPRING ST, NEW YORK, NY 10013 USA SN 0020-9910 J9 INVENT MATH JI Invent. Math. PD OCT PY 2009 VL 178 IS 1 BP 119 EP 171 DI 10.1007/s00222-009-0196-4 PG 53 SC Mathematics GA 498WC UT ISI:000270175100004 ER EF Record 4 of 5: FN ISI Export Format VR 1.0 PT J AU Hacking, P Keel, S Tevelev, J AF Hacking, Paul Keel, Sean Tevelev, Jenia TI Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces SO INVENTIONES MATHEMATICAE LA English DT Article ID N-POINTED CURVES; PLANE-CURVES; GENUS ZERO; VARIETIES; QUOTIENTS; GEOMETRY; THREEFOLDS AB We give a functorial normal crossing compactification of the moduli space of smooth cubic surfaces entirely analogous to the Grothendieck-Knudsen compactification M-0,M-n subset of (M-0,M-n) over bar. C1 [Hacking, Paul] Univ Washington, Dept Math, Seattle, WA 98195 USA. [Keel, Sean] Univ Texas Austin, Dept Math, Austin, TX 78712 USA. [Tevelev, Jenia] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA. RP Hacking, P, Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA. EM hacking@math.washington.edu keel@math.utexas.edu tevelev@math.umass.edu FU NSF [DMS-0650052, DMS-0353994, DMS-0701191] FX Daniel Allcock helped us a great deal with the branch cover constructions of Sect. 4. We thank A.-M. Castravet, I. Dolgachev, B. Fantechi, G. Farkas, S. Grushevskii, B. Hassett, G. Heckmann, R. Heitmann, J. Kollar, M. Luxton, M. Olsson, Z. Qu, M. Reid, B. Sturmfels, and L. Williams for many helpful discussions. We are particularly grateful to Professor Jiro Sekiguchi for sending us copies of his (quite remarkable) papers, from which we got a great deal of combinatorial inspiration. The first author was partially supported by NSF grant DMS-0650052, the second author by NSF grant DMS-0353994, and the third author by NSF grant DMS-0701191 and a Sloan research fellowship. NR 52 TC 0 PU SPRINGER PI NEW YORK PA 233 SPRING ST, NEW YORK, NY 10013 USA SN 0020-9910 J9 INVENT MATH JI Invent. Math. PD OCT PY 2009 VL 178 IS 1 BP 173 EP 227 DI 10.1007/s00222-009-0199-1 PG 55 SC Mathematics GA 498WC UT ISI:000270175100005 ER EF Record 5 of 5: FN ISI Export Format VR 1.0 PT J AU Ballinger, B Blekherman, G Cohn, H Giansiracusa, N Kelly, E Schurmann, A AF Ballinger, Brandon Blekherman, Grigoriy Cohn, Henry Giansiracusa, Noah Kelly, Elizabeth Schurmann, Achill TI Experimental Study of Energy-Minimizing Point Configurations on Spheres SO EXPERIMENTAL MATHEMATICS LA English DT Article DE Energy minimization; polytopes; universal optimality ID MINIMUM LATTICE CONFIGURATIONS; GRAIN-BOUNDARY SCARS; THOMSONS PROBLEM; ASSOCIATION SCHEMES; RIESZ ENERGY; UNIQUENESS; CHARGES; DISLOCATIONS; ASYMPTOTICS; CODES AB In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima. C1 [Ballinger, Brandon] Google Inc, Mountain View, CA 94043 USA. [Blekherman, Grigoriy] Microsoft Res, Redmond, WA 98052 USA. [Cohn, Henry] Microsoft Res New England, Cambridge, MA 02142 USA. [Giansiracusa, Noah] Brown Univ, Dept Math, Providence, RI 02912 USA. [Kelly, Elizabeth] Univ Washington, Dept Math, Seattle, WA 98195 USA. [Schurmann, Achill] Delft Univ Technol, Inst Appl Math, NL-2628 CD Delft, Netherlands. RP Ballinger, B, Google Inc, 1600 Amphitheatre Pkwy, Mountain View, CA 94043 USA. EM brandonb@google.com grrigg@gmail.com cohn@microsoft.com noahgian@math.brown.edu thebethkelly@gmail.com a.schurmann@tudelft.nl FU Deutsche Forschungsgemeinschaft (DFG) [SCHU 1503/4-1] FX We thank Eiichi Bannai, Christian Borgs, John Conway, Edwin van Dam, Charles Doran, Noam Elkies, Florian Gaisendrees, Robert Griess, Abhinav Kumar, Jaron Lanier, James Morrow, Frank Stillinger, and Salvatore Torquato for helpful discussions. Ballinger and Giansiracusa were supported by the University of Washington Mathematics Department's NSF VI-GRE grant. Schurmann was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4-1. NR 53 TC 0 PU A K PETERS LTD PI WELLESLEY PA 888 WORCESTER STREET, STE 230, WELLESLEY, MA 02482-3748 USA SN 1058-6458 J9 EXP MATH JI Exp. Math. PY 2009 VL 18 IS 3 BP 257 EP 283 PG 27 SC Mathematics GA 497PU UT ISI:000270073200001 ER EF
