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Theory and Methods

Bayesian Inference Using Synthetic Likelihood: Asymptotics and Adjustments

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Pages 2821-2832 | Received 12 Mar 2021, Accepted 30 May 2022, Published online: 11 Jul 2022

References

  • An, Z., Nott, D. J., and Drovandi, C. (2020), “Robust Bayesian Synthetic Likelihood via a Semi-parametric Approach,” Statistics and Computing, 30, 543–557. DOI: 10.1007/s11222-019-09904-x.
  • An, Z., South, L. F., Drovandi, C. C., and Nott, D. J. (2019), “Accelerating Bayesian Synthetic Likelihood with the Graphical Lasso,” Journal of Computational and Graphical Statistics, 28, 471–475. DOI: 10.1080/10618600.2018.1537928.
  • Andrieu, C., and Roberts, G. O. (2009), “The Pseudo-Marginal Approach for Efficient Monte Carlo Computations,” The Annals of Statistics, 37, 697–725. DOI: 10.1214/07-AOS574.
  • Beaumont, M. A., Zhang, W., and Balding, D. J. (2002), “Approximate Bayesian Computation in Population Genetics,” Genetics, 162, 2025–2035. DOI: 10.1093/genetics/162.4.2025.
  • Bissiri, P. G., Holmes, C. C., and Walker, S. G. (2016), “A General Framework for Updating Belief Distributions,” Journal of the Royal Statistical Society, Series B, 78, 1103–1130. DOI: 10.1111/rssb.12158.
  • Chaudhuri, S., Ghosh, S., Nott, D. J., and Pham, K. C. (2020), “On a Variational Approximation Based Empirical Likelihood ABC Method,” arXiv:2011.07721.
  • Chernozhukov, V., and Hong, H. (2003), “An MCMC Approach to Classical Estimation,” Journal of Econometrics, 115, 293–346. DOI: 10.1016/S0304-4076(03)00100-3.
  • Deligiannidis, G., Doucet, A., and Pitt, M. K. (2018), “The Correlated Pseudo-Marginal Method,” Journal of the Royal Statistical Society, Series B, 80, 839–870. DOI: 10.1111/rssb.12280.
  • Doucet, A., Pitt, M. K., Deligiannidis, G., and Kohn, R. (2015), “Efficient Implementation of Markov chain Monte Carlo When Using an Unbiased Likelihood Estimator,” Biometrika, 102, 295–313. DOI: 10.1093/biomet/asu075.
  • Drovandi, C. C., Pettitt, A. N., and Lee, A. (2015), “Bayesian Indirect Inference Using a Parametric Auxiliary Model,” Statistical Science, 30, 72–95. DOI: 10.1214/14-STS498.
  • Everitt, R. G. (2017), “Boostrapped Synthetic Likelihood,” arXiv:1711. 05825.
  • Fasiolo, M., Wood, S. N., Hartig, F., and Bravington, M. V. (2018), “An Extended Empirical Saddlepoint Approximation for Intractable Likelihoods,” Electronic Journal of Statistics, 12, 1544–1578. DOI: 10.1214/18-EJS1433.
  • Forneron, J.-J., and Ng, S. (2018), “The ABC of Simulation Estimation with Auxiliary Statistics,” Journal of Econometrics, 205, 112–139. DOI: 10.1016/j.jeconom.2018.03.007.
  • Frazier, D. T., and Drovandi, C. (2021), “Robust Approximate Bayesian Inference with Synthetic Likelihood,” Journal of Computational and Graphical Statistics, 30, 958–976. DOI: 10.1080/10618600.2021.1875839.
  • Frazier, D. T., Martin, G. M., Robert, C. P., and Rousseau, J. (2018), “Asymptotic Properties of Approximate Bayesian Computation,” Biometrika, 105, 593–607. DOI: 10.1093/biomet/asy027.
  • Frazier, D. T., Robert, C. P., and Rousseau, J. (2020), “Model Misspecification in Approximate Bayesian Computation: Consequences and Diagnostics,” Journal of the Royal Statistical Society, Series B, 82, 421–444. DOI: 10.1111/rssb.12356.
  • 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.
  • Hannan, E. J. (1976), “The Asymptotic Distribution of Serial Covariances,” The Annals of Statistics, 4, 396–399. DOI: 10.1214/aos/1176343415.
  • Kong, A. (1992), “A Note on Importance Sampling Using Standardized Weights,” Chicago Department of Statistics Technical Report 348.
  • Kreiss, J.-P., and Paparoditis, E. (2011), “Bootstrap Methods for Dependent Data: A Review,” Journal of the Korean Statistical Society, 40, 357–378. DOI: 10.1016/j.jkss.2011.08.009.
  • Li, W., and Fearnhead, P. (2018a), “Convergence of Regression-Adjusted Approximate Bayesian Computation,” Biometrika, 105, 301–318. DOI: 10.1093/biomet/asx081.
  • Li, W., and Fearnhead, P. (2018b), “On the Asymptotic Efficiency of Approximate Bayesian Computation Estimators,” Biometrika, 105, 285–299.
  • Marchand, P., Boenke, M., and Green, D. M. (2017), “A Stochastic Movement Model Reproduces Patterns of Site Fidelity and Long-Distance Dispersal in a Population of Fowler’s Toads (Anaxyrus fowleri),” Ecological Modelling, 360, 63–69. DOI: 10.1016/j.ecolmodel.2017.06.025.
  • McKay, M., Beckman, R., and Conover, W. (1979), “Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, 21, 239–245.
  • Meeds, E., and Welling, M. (2014), “GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation,” in Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, UAI’14, Arlington, VA, pp. 593–602. AUAI Press.
  • Mengersen, K. L., Pudlo, P., and Robert, C. P. (2013), “Bayesian Computation via Empirical Likelihood,” Proceedings of the National Academy of Sciences, 110, 1321–1326. DOI: 10.1073/pnas.1208827110.
  • Müller, U. K. (2013), “Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix,” Econometrica, 81, 1805–1849.
  • Ong, V. M.-H., Nott, D. J., Tran, M.-N., Sisson, S., and Drovandi, C. (2018a), “Variational Bayes with Synthetic Likelihood,” Statistics and Computing, 28, 971–988. DOI: 10.1007/s11222-017-9773-3.
  • Ong, V. M.-H., Nott, D. J., Tran, M.-N., Sisson, S., and Drovandi, C. (2018b), “Likelihood-Free Inference in High Dimensions with Synthetic Likelihood,” Computational Statistics and Data Analysis, 128, 271–291.
  • Pitt, M. K., Silva, R. d. S., Giordani, P., and Kohn, R. (2012), “On Some Properties of Markov chain Monte Carlo Simulation Methods Based on the Particle Filter,” Journal of Econometrics, 171, 134–151. DOI: 10.1016/j.jeconom.2012.06.004.
  • Price, L. F., Drovandi, C. C., Lee, A. C., and Nott, D. J. (2018), “Bayesian Synthetic Likelihood,” Journal of Computational and Graphical Statistics, 27, 1–11. DOI: 10.1080/10618600.2017.1302882.
  • Priddle, J. W., Sisson, S. A., Frazier, D. T., Turner, I., and Drovandi, C. (2022), “Efficient Bayesian Synthetic Likelihood with Whitening Transformations,” Journal of Computational and Graphical Statistics, 31, 50–63. DOI: 10.1080/10618600.2021.1979012.
  • Sherlock, C., Thiery, A. H., Roberts, G. O., and Rosenthal, J. S. (2015), “On the Efficiency of Pseudo-Marginal Random Walk Metropolis Algorithms,” The Annals of Statistics, 43, 238–275. DOI: 10.1214/14-AOS1278.
  • Sisson, S. A., Fan, Y., and Beaumont, M. (2018), Handbook of Approximate Bayesian Computation, Boca Raton, FL: Chapman and Hall/CRC.
  • Thomas, O., Dutta, R., Corander, J., Kaski, S., and Gutmann, M. U. (2022), “Likelihood-Free Inference by Ratio Estimation,” Bayesian Analysis, 17, 1–31. DOI: 10.1214/20-BA1238.
  • Tran, M.-N., Kohn, R., Quiroz, M., and Villani, M. (2016), “The Block Pseudo-Marginal Sampler,” arXiv preprint arXiv:1603.02485.
  • Vershynin, R. (2018), High-Dimensional Probability: An Introduction with Applications in Data Science (Vol. 47), Cambridge: Cambridge University Press.
  • Warton, D. I. (2008), “Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices,” Journal of the American Statistical Association, 103, 340–349. DOI: 10.1198/016214508000000021.
  • Wilkinson, R. (2014), “Accelerating ABC Methods Using Gaussian Processes,” Journal of Machine Learning Research, 33, 1015–1023.
  • Wood, S. N. (2010), “Statistical Inference for Noisy Nonlinear Ecological Dynamic Systems,” Nature, 466, 1102–1107. DOI: 10.1038/nature09319.