600
Views
9
CrossRef citations to date
0
Altmetric
Bayesian Computing

Improving Approximate Bayesian Computation via Quasi-Monte Carlo

&
Pages 205-219 | Received 01 Oct 2017, Published online: 17 Oct 2018

References

  • Agapiou, S., Papaspiliopoulos, O., Sanz-Alonso, D., and Stuart, A. M. (2017), “Importance Sampling: Computational Complexity and Intrinsic Dimension,” Statistical Science, 32, 405–431.
  • Andrieu, C., and Roberts, G. O. (2009), “The Pseudo-Marginal Approach for Efficient Monte Carlo Computations,” Annals of Statistics, 37, 697–725.
  • Barthelmé, S., and Chopin, N. (2014), “Expectation Propagation for Likelihood-Free Inference,” Journal of the American Statistical Association, 109, 315–333.
  • Beaumont, M. A., Cornuet, J.-M., Marin, J.-M., and Robert, C. P. (2009), “Adaptive Approximate Bayesian Computation,” Biometrika, 96, 983–990.
  • Bernton, E., Jacob, P. E., Gerber, M., and Robert, C. P. (2017), “Inference in Generative Models using the Wasserstein Distance,” arXiv preprint arXiv:1701.05146.
  • Blei, D. M., Kucukelbir, A., and McAuliffe, J. D. (2017), “Variational Inference: A Review for Statisticians,” Journal of the American Statistical Association, 112, 859–877.
  • Blum, M. G. (2010), “Approximate Bayesian Computation: A Nonparametric Perspective,” Journal of the American Statistical Association, 105, 1178–1187.
  • Bornn, L., Pillai, N. S., Smith, A., and Woodard, D. (2015), “The Use of a Single Pseudo-Sample in Approximate Bayesian Computation,” Statistics and Computing, 27, 1–14.
  • Chalabi, Y., Dutang, C., Savicky, P., Wuertz, D., Matsumoto, M., Saito, M., and Knuth, D. (2018), “Randtoolbox: Generating and Testing Random Numbers,” R Package Version 1.17, available at https://cran.r-project.org/web/packages/randtoolbox
  • Del Moral, P., Doucet, A., and Jasra, A. (2012), “An Adaptive Sequential Monte Carlo Method for Approximate Bayesian Computation,” Statistics and Computing, 22, 1009–1020.
  • Dick, J., Kuo, F. Y., and Sloan, I. H. (2013), “High-Dimensional Integration: The Quasi-Monte Carlo Way,” Acta Numerica, 22, 133–288.
  • Dick, J., and Pillichshammer, F. (2010), Digital Nets and Sequences: Discrepancy Theory and Quasi–Monte Carlo Integration, Cambridge: Cambridge University Press.
  • Fearnhead, P., and Prangle, D. (2012), “Constructing Summary Statistics for Approximate Bayesian Computation: Semi-Automatic Approximate Bayesian Computation,” Journal of the Royal Statistical Society, Series B, 74, 419–474.
  • Gerber, M. (2015), “On Integration Methods Based on Scrambled Nets of Arbitrary Size,” Journal of Complexity, 31, 798–816.
  • Gerber, M., and Chopin, N. (2015), “Sequential Quasi Monte Carlo,” Journal of the Royal Statistical Society, Series B, 77, 509–579.
  • Glasserman, P. (2013), Monte Carlo Methods in Financial Engineering (Vol. 53), New York: Springer Science & Business Media.
  • Gutmann, M. U., and Corander, J. (2016), “Bayesian Optimization for Likelihood-free Inference of Simulator-based Statistical Models,” Journal of Machine Learning Research, 17, 1–47.
  • Hardy, G. H. (1905), “On Double Fourier Series, and Especially Those Which Represent the Double Zeta-function with Real and Incommensurable Parameters,” Quarterly Journal of Mathematics, 37, 53–79.
  • Hickernell, F. J. (2006), Koksma–Hlawka Inequality, American Cancer Society, Encyclopedia of Statistical Sciences, Wiley.
  • Johnson, N. L., Kemp, A. W., and Kotz, S. (2005), Univariate Discrete Distributions (Vol. 444), New York: Wiley.
  • Kong, A., Liu, J. S., and Wong, W. H. (1994), “Sequential Imputation and Bayesian Missing Data Problems,” Journal of the American Statistical Association, 89, 278–288.
  • Kuipers, L., and Niederreiter, H. (2012), Uniform Distribution of Sequences, Courier Corporation, Dover Publications.
  • L’Ecuyer, P. (2016), “Randomized Quasi-Monte Carlo: An Introduction for Practitioners,” in 12th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2016).
  • Lee, A. (2012), “On the Choice of MCMC Kernels for Approximate Bayesian Computation with SMC Samplers,” in Simulation Conference (WSC), Proceedings of the 2012 Winter, IEEE, pp. 1–12.
  • Lee, A., and Łatuszyński, K. (2014), “Variance Bounding and Geometric Ergodicity of Markov Chain Monte Carlo Kernels for Approximate Bayesian Computation,” Biometrika, 101, 655–671.
  • Leobacher, G., and Pillichshammer, F. (2014), Introduction to Quasi-Monte Carlo Integration and Applications, New York: Springer.
  • Lintusaari, J., Gutmann, M. U., Dutta, R., Kaski, S., and Corander, J. (2017), “Fundamentals and Recent Developments in Approximate Bayesian Computation,” Systematic Biology, 66, e66–e82.
  • Marin, J.-M., Pudlo, P., Robert, C., and Ryder, R. (2012), “Approximate Bayesian Computational Methods,” Statistics and Computing, 22, 1167–1180.
  • Marin, J.-M., Raynal, L., Pudlo, P., Ribatet, M., and Robert, C. P. (2016), “ABC Random Forests for Bayesian Parameter Inference,” arXiv preprint arXiv:1605.05537.
  • Marjoram, P., Molitor, J., Plagnol, V., and Tavare, S. (2003), “Markov Chain Monte Carlo Without Likelihoods,” Proceedings of the National Academy of Sciences of the United States of America, 100, 15324–15328.
  • Niederreiter, H. (1978), “Quasi-Monte Carlo Methods and Pseudo-random Numbers,” Bulletin of the American Mathematical Society, 84, 957–1041.
  • Ökten, G., Tuffin, B., and Burago, V. (2006), “A Central Limit Theorem and Improved Error Bounds for a Hybrid-Monte Carlo Sequence with Applications in Computational Finance,” Journal of Complexity, 22, 435–458.
  • Owen, A. B. (1997), “Scrambled Net Variance for Integrals of Smooth Functions,” The Annals of Statistics, 25, 1541–1562.
  • ——— (1998), “Monte Carlo Extension of Quasi-Monte Carlo,” in 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274) (Vol. 1), IEEE Computer Society Press Los Alamitos, pp. 571–577.
  • ——— (2008), “Local Antithetic Sampling with Scrambled Nets,” The Annals of Statistics, 36, 2319–2343.
  • Papamakarios, G., and Murray, I. (2016), “Fast ϵ-free Inference of Simulation Models with Bayesian Conditional Density Estimation,” in Advances in Neural Information Processing Systems, pp. 1028–1036, available at https://papers.nips.cc/
  • Sedki, M., Pudlo, P., Marin, J.-M., Robert, C. P., and Cornuet, J.-M. (2012), “Efficient Learning in ABC Algorithms,” arXiv preprint 1210.1388.
  • Sisson, S. A., Fan, Y., Tanaka, M. M., Rogers, A., Huang, Y., Njegic, B., Wayne, L., Gordon, M. S., Dabdub, D., Gerber, R. B., and Finlayson-pitts, B. J. (2009), “Correction for Sisson et al., Sequential Monte Carlo without Likelihoods,” Proceedings of the National Academy of Sciences, 106, 16889–16889.
  • Tanaka, M. M., Francis, A. R., Luciani, F., and Sisson, S. A. (2006), “Using Approximate Bayesian Computation to Estimate Tuberculosis Transmission Parameters from Genotype Data,” Genetics, 173, 1511–1520.
  • Tavaré, S., Balding, D. J., Griffiths, R. C., and Donnelly, P. (1997), “Inferring Coalescence Times from DNA Sequence Data,” Genetics, 145, 505–518.
  • Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. P. (2009), “Approximate Bayesian Computation Scheme for Parameter Inference and Model Selection in Dynamical Systems,” Journal of The Royal Society Interface, 6, 187–202.
  • Wilkinson, R. D. (2014), “Accelerating ABC Methods Using Gaussian Processes,” in Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS) (Vol. 33), pp. 1015–1023, available at http://proceedings.mlr.press/v84/

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.