287
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Bayesian inversion by parallel interacting Markov chains

Pages 111-130 | Received 15 Oct 2008, Accepted 19 Feb 2009, Published online: 22 Sep 2009

References

  • Tarantola, A, 2005. Inverse Problem Theory and Model Parameter Estimation. Philadelphia: SIAM; 2005.
  • Kitanidis, PK, 1995. Quasi-linear geostatistical theory for inversing, Water Resour. Res. 31 (1995), pp. 2411–2419.
  • Oliver, DS, 1996. On conditional simulation to inaccurate data, Math. Geol. 28 (1996), pp. 811–817.
  • Sambridge, M, 1999. Geophysical inversion with a neighbourhood algorithm: I. Searching a parameter space, Geophys. J. Int. 138 (1999), pp. 479–494.
  • Sambridge, M, 1999. Geophysical inversion with a neighbourhood algorithm: II. Appraising the ensemble, Geophys. J. Int. 138 (1999), pp. 727–746.
  • Robert, CP, and Casella, G, 2004. Monte-Carlo Statistical Methods, . Berlin: Springer; 2004.
  • Romary, T, 2009. Integrating production data under uncertainty by parallel interacting Markov chains on a reduced dimensional space, Comput. Geosci. 13 (2009), pp. 103–122.
  • Metropolis, N, Rosenbluth, A, Rosenbluth, M, and Teller, ATM, 1953. Equations of state calculations by fast computing machines, J. Chem. Phys. 21 (1953), pp. 1087–1091.
  • Meyn, SP, and Tweedie, RL, 1993. Markov Chains and Stochastic Stability. Berlin: Springer; 1993.
  • Stramer, O, and Tweedie, RL, 1999. Self-targeting candidates for Metropolis–Hastings algorithms, Method. Comput. Appl. Probab. 16 (1999), pp. 307–328.
  • Roberts, GO, and Rosenthal, JS, 1998. Optimal scaling of discrete approximations to Langevin diffusions, J. Roy. Stat. Soc. B 60 (1998), pp. 255–268.
  • Haario, H, Saksman, E, and Tamminen, J, 2001. An adaptive Metropolis algorithm, Bernoulli 7 (2001), pp. 223–242.
  • Andrieu, C, and Robert, CP, 2001. "Controlled MCMC for optimal sampling". In: Tech. Rep., Cérémade. DAUPHINE: Université de PARIS; 2001.
  • Andrieu, C, and Moulines, E, 2003. On the ergodicity properties of some adaptive MCMC algorithms, Annals Appl. Probab. 16 (2003), pp. 1462–1505.
  • Kirkpatrick, S, Gelatt, CD, and Vecchi, MP, 1983. Optimization by simulated annealing, Science 220 (1983), pp. 671–680.
  • Marinari, E, and Parisi, G, 1992. Simulated tempering: A new Monte-Carlo scheme, Europhy. Lett. 19 (1992), pp. 451–458.
  • Geyer, CJ, and Thompson, EA, 1995. Annealing Markov chain Monte-Carlo with applications to ancestral inference, J. Amer. Stat. Assoc. 90 (1995), pp. 909–920.
  • Celeux, G, Hurn, M, and Robert, CP, 1999. Computational and inferential difficulties with mixture posterior distributions, Tech. Rep. RR-3627, INRIA (1999).
  • Geyer, CJ, 1991. "Markov chain Monte-Carlo maximum likelihood". In: Computing science and statistics: Proceedings of 23rd symposium on the interface interface foundation. New York: Fairfax Station; 1991. p. 156.
  • Earl, DJ, and Deem, MW, 2005. Parallel tempering : Theory, applications, and new perspectives, Phys. Chem. Chem. Phys. 7 (2005), pp. 3910–3916.
  • Iba, Y, 2001. Extended ensemble Monte-Carlo, Int. J. Modern Phys. C 12 (2001), pp. 623–656.
  • Kou, SC, Zhou, Q, and Wong, WH, 2006. Equi-energy sampler with applications in statistical inference and statistical mechanics, Annals Stat. 34 (2006), pp. 1581–1619.
  • Andrieu, C, Jasra, A, Doucet, A, and Del Moral, P, 2007. On non-linear Markov chain Monte-Carlo via self-interacting approximations. Tech. Rep.. University of Bristol; 2007.
  • Tierney, L, 1994. Markov chains for exploring posterior distributions, Annals Stat. 22 (1994), pp. 1701–1762.
  • Chilés, JP, and Delfiner, P, 1999. Geostatistics, Modeling Spatial Uncertainty. New York: John Wiley & Sons; 1999.
  • Strebelle, S, 2002. Conditional simulation of complex geological structures using multiple-point geostatistics, Math. Geol. 34 (2002), pp. 1–22.
  • Lantuéjoul, C, 2002. Geostatistical Simulation. Berlin: Springer; 2002.
  • 3dsl User Manual, StreamSim Technologies, Inc. Version 3.00 ed., 2008. www.streamsim.com.
  • Romary, T, and Hu, LY, 2007. Assessing the dimensionality of random fields with Karhunen–Loéve expansion, in Petroleum Geostatistics 2007 (2007), Cascais, Portugal.
  • Romary, T, and Hu, LY, 2008. "History matching of truncated Gaussian models by parallel interacting Markov chains on a reduced dimensional space". In: ECMOR XI, 11th European Conference on the Mathematics of Oil Recovery. Bergen, Norway. 2008.
  • Loéve, M, 1955. Probability Theory. New York: Van Nostrand; 1955.
  • Higdon, D, Lee, H, and Bi, Z, 2002. A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine-scale information, IEEE Trans. Signal Process. 50 (2002), pp. 389–399.
  • Balakrishnan, S, Roy, A, Ierapetritou, MG, Flach, GP, and Georgopoulos, PG, 2003. Uncertain reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method, Water Resour. Res. 39 (2003), p. 1350.
  • Jin, B, 2008. Fast Bayesian approach for parameter estimation, Int. J. Numer. Methods Eng. 76 (2008), pp. 230–252.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.