Parameter estimation in high dimensional Gaussian distributions

• Al-Mohy, A., Higham, N.: Computing the action of the matrix exponential, with an application to exponential integrators. Technical report, University of Manchester (2011)

• Anitescu, M., Chen, J., Wang, L.: A matrix-free approach for solving the Gaussian process maximum likelihood problem. SIAM J. Sci. Comput. 34, A240–A262 (2012)

  Article  MATH  MathSciNet  Google Scholar 

• Aune, E., Eidsvik, J., Pokern, Y.: Iterative numerical methods for sampling from high dimensional Gaussian distributions. Stat. Comput. (2012, forthcoming). doi:10.1007/s11222-012-9326-8

• Bai, Z., Fahey, G., Golub, G.: Some large-scale matrix computation problems. J. Comput. Appl. Math. 74(1), 71–89 (1996)

  Article  MATH  MathSciNet  Google Scholar 

• Bai, Z., Golub, G.: Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Ann. Numer. Math. 4, 29–38 (1997)

  MATH  MathSciNet  Google Scholar 

• Bekas, C., Kokiopoulou, E., Saad, Y.: An estimator for the diagonal of a matrix. Appl. Numer. Math. 57(11–12), 1214–1229 (2007)

  Article  MATH  MathSciNet  Google Scholar 

• Benzi, M., Golub, G.: Bounds for the entries of matrix functions with applications to preconditioning. BIT Numer. Math. 39(3), 417–438 (1999)

  Article  MATH  MathSciNet  Google Scholar 

• Benzi, M., Razouk, N.: Decay bounds and \(\mathcal{O}(n)\) algorithms for approximating functions of sparse matrices. Electron. Trans. Numer. Anal. 28, 16–39 (2007)

  MATH  MathSciNet  Google Scholar 

• Besag, J.: Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc. B 36, 192–236 (1974)

  MATH  MathSciNet  Google Scholar 

• Bolin, D., Lindgren, F.: Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping. Ann. Appl. Stat. 5(1), 523–550 (2011)

  Article  MATH  MathSciNet  Google Scholar 

• Buland, A., Omre, H.: Bayesian linearized AVO inversion. Geophysics 68, 185–198 (2003)

  Article  Google Scholar 

• Candès, E., Demanet, L., Donoho, D., Ying, L.: Fast discrete curvelet transforms. Multiscale Model. Simul. 5(3), 861–899 (2006)

  Article  MATH  MathSciNet  Google Scholar 

• Chan, T., Tang, W., Wan, W.: Wavelet sparse approximate inverse preconditioners. BIT Numer. Math. 37(3), 644–660 (1997)

  Article  MATH  MathSciNet  Google Scholar 

• Chen, Y., Davis, T., Hager, W., Rajamanickam, S.: Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Trans. Math. Softw. 35(3), 22 (2008)

  Article  MathSciNet  Google Scholar 

• Cressie, N.: Statistics for Spatial Data. Wiley, New York (1993)

  Google Scholar 

• Cressie, N., Johannesson, G.: Fixed rank kriging for large spatial datasets. J. R. Stat. Soc. B 70, 209–226 (2008)

  Article  MATH  MathSciNet  Google Scholar 

• Culberson, J.: Iterated greedy graph coloring and the difficulty landscape. Technical report, University of Alberta (1992)

• Davies, P.I., Higham, N.J.: Computing f(A)b for matrix functions f In: QCD and Numerical Analysis III, pp. 15–24. Springer, Berlin (2005)

  Chapter  Google Scholar 

• Davis, T., Hager, W.: Modifying a sparse Cholesky factorization. SIAM J. Matrix Anal. Appl. 20(3), 606–627 (1999)

  Article  MATH  MathSciNet  Google Scholar 

• Driscoll, A.: The Schwarz Christoffel Toolbox (2009). Available at http://www.math.udel.edu/~driscoll/software/SC. Electronic

• Eidsvik, J., Shaby, B.A., Reich, B.J., Wheeler, M., Niemi, J.: Estimation and prediction in spatial models with block composite likelihoods using parallel computing. Technical report, NTNU (2011)

• Estrada, E., Hatano, N., Benzi, M.: The physics of communicability in complex networks (2011). Arxiv preprint arXiv:1109.2950

• Frommer, A.: BiCGStab (l) for families of shifted linear systems. Computing 70(2), 87–109 (2003)

  Article  MATH  MathSciNet  Google Scholar 

• Fuentes, M.: Approximate likelihood for large irregularly spaced spatial data. J. Am. Stat. Assoc. 102(477), 321–331 (2007)

  Article  MATH  MathSciNet  Google Scholar 

• Gorjanc, G.: Graphical model representation of pedigree based mixed model. In: 32nd International Conference on Information Technology Interfaces (ITI), 2010, pp. 545–550. IEEE Press, New York (2010)

  Google Scholar 

• Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Basel (2001)

  Book  MATH  Google Scholar 

• Hale, N., Higham, N.J., Trefethen, L.N.: Computing A ^α, log(A) and related matrix functions by contour integrals. SIAM J. Numer. Anal. 46, 2505–2523 (2008)

  Article  MATH  MathSciNet  Google Scholar 

• Higham, N.J.: Functions of Matrices: Theory and Computation. SIAM, Philadelphia (2008)

  Book  Google Scholar 

• Huckle, M., Grote, M.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18(3), 838–853 (1997)

  Article  MATH  MathSciNet  Google Scholar 

• Hutchinson, M.: A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. Commun. Stat., Simul. Comput. 18, 1059–1076 (1989)

  Article  MATH  MathSciNet  Google Scholar 

• Jegerlehner, B.: Krylov space solvers for shifted linear systems (1996). arXiv:hep-lat/9612014v1

• Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359 (1999)

  Article  MATH  MathSciNet  Google Scholar 

• Lindgren, F., Lindstrøm, J., Rue, H.: An explicit link between Gaussian fields and Gaussian Markov random fields: the SPDE approach. J. R. Stat. Soc. B 73, 423–498 (2011)

  Article  MATH  Google Scholar 

• Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, San Diego (1998)

  MATH  Google Scholar 

• MATLAB (2010). Version 7.11.0 (R2010b). The MathWorks Inc., Natick, Massachusetts

• McPeters, R., Aeronautics, U.S.N., Scientific, S.A., Branch, T.I.: Nimbus-7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide. NASA, Scientific and Technical Information Branch (1996)

• Rue, H., Held, L.: Gaussian Markov Random Fields. Chapman & Hall, London (2005)

  Book  MATH  Google Scholar 

• Rue, H., Martino, S., Chopin, N.: Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc., Ser. B, Stat. Methodol. 71(2), 319–392 (2009)

  Article  MATH  MathSciNet  Google Scholar 

• Rue, H., Tjelmeland, H.: Fitting Gaussian Markov random fields to Gaussian fields. Scand. J. Stat. 29, 31–49 (2002)

  Article  MATH  MathSciNet  Google Scholar 

• Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003)

  Book  MATH  Google Scholar 

• Simpson, D.: Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion. Ph.D. thesis, School of Mathematical Sciences, Queensland Univ. of Tech. (2008)

• Simpson, D., Turner, I., Pettitt, A.: Fast sampling from a Gaussian Markov random field using Krylov subspace approaches. Technical report, School of Mathematical Sciences, Queensland Univ. of Tech. (2008)

• Stein, M., Chen, J., Anitescu, M.: Stochastic approximation of score functions for Gaussian processes. Technical report (2012). Preprint ANL/MCSP-2091-0512

• Tang, J., Saad, Y.: A probing method for computing the diagonal of the matrix inverse. Technical report, Minnesota Supercomputing Institute for Advanced Computational Research (2010)

• van der Vorst, H., Melissen, J.: A Petrov-Galerkin type method for solving A×k=b, where A is symmetric complex. IEEE Trans. Magn. 26(2), 706–708 (1990)

  Article  Google Scholar 

Download references