Polynomial Accelerated MCMC and Other Sampling Algorithms Inspired by Computational Optimization

Springer Proceedings in Mathematics and Statistics

Volumn 65, Issue , 2013, Pages 349-366

  Fox, Colin ^a  

^a UNIVERSITY OF OTAGO   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION METHOD; CHEBYSHEV ACCELERATION; COMPUTATIONAL OPTIMIZATION; EXACT ARITHMETIC; GIBBS SAMPLING; MATRIX SPLITTINGS; SAMPLING ALGORITHM;

CONJUGATE GRADIENT METHOD; GAUSSIAN DISTRIBUTION; MONTE CARLO METHODS;

OPTIMIZATION;

EID: 84893484935     PISSN: 21941009     EISSN: 21941017     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-642-41095-6_15     Document Type: Conference Paper

References (22)

1. Adler, S.L.: Over-relaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions. Phys. Rev. D 23, 2901-2904 (1981)
2. Amit, Y., Grenander, U.: Comparing sweep strategies for stochastic relaxation. J. Multivariate Anal. 37, 197-222 (1991)
3. Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge (1996)
4. Barone, P., Frigessi, A.: Improving stochastic relaxation for Gaussian random fields. Probab. Engrg. Inform. Sci. 4, 369-384 (1990)
5. Ceriotti, M., Bussi, G., Parrinello, M.: Conjugate gradient heat bath for ill-conditioned actions. Phys. Rev. E 76, 026707-1-8 (2007)
6. Diaconis, P., Freedman, D.: Iterated random functions. SIAM Rev. 41, 45-76 (1999)
7. Fox, C.: A conjugate direction sampler for normal distributions, with a few computed examples. Technical Reports from the Electronics Group, University of Otago (2008)
8. Fox, C., Parker, A.: Convergence in variance of Chebyshev accelerated Gibbs samplers. SIAM J. Sci. Comput. (2013, to appear)
9. Fox, C., Parker, A.: Gibbs sampling of normal distributions using matrix splittings and polynomial acceleration. (2013, in preparation)
10. Galli, A., Gao, H.: Rate of convergence of the Gibbs sampler in the Gaussian case. Mathematical Geology 33, 653-677 (2001)
11. Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741 (1984)
12. Glauber, R.: Time dependent statistics of the Ising model. J. Math. Phys. 4, 294-307 (1963)
13. Golub, G.H., Varga, R.S.: Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, parts I and II. Numer. Math. 3, 147-156, 157-168 (1961)
14. Goodman, J., Sokal, A.D.:MultigridMonte Carlo method. Conceptual foundations. Phys. Rev. D 40, 2035-2071 (1989)
15. Higdon, D.: A primer on space-time modelling from a Bayesian perspective. In: Finkenstadt, B., Held, L., Isham, V. (eds.) Statistics of Spatio-Temporal Systems, pp. 217-279. Chapman & Hall/CRC, New York (2006)
16. Łatuszyński, K., Roberts, G.O.: CLTs and asymptotic variance of time-sampledMarkov chains. Methodol. Comput. Appl. Probab. 15, 237-247 (2013)
17. Parker, A., Fox, C.: Sampling Gaussian distributions in Krylov spaces with conjugate gradients. SIAM J. Sci. Comput. 34, B312-B334 (2012)
18. Roberts, G.O., Sahu, S.K.: Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J. R. Stat. Soc. Ser. B. 59, 291-317 (1997)
19. Rue, H.: Fast sampling of Gaussian Markov random fields. J. R. Stat. Soc. Ser. B. 63, 325-338 (2001)
20. Schneider, M.K., Willsky, A.S.: A Krylov subspace method for covariance approximation and simulation of random processes and fields. Multidimens. Syst. Signal Process. 14, 295-318 (2003)
21. Turchin, V.F.: On the computation of multidimensional integrals by the Monte Carlo method. Theory Probab. Appl. 16, 720-724 (1971)
22. Young, D.M.: Iterative Solution of Large Linear Systems. Academic, New York (1971)