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General

Likelihood-Free Parameter Estimation with Neural Bayes Estimators

ORCID Icon, ORCID Icon & ORCID Icon
Pages 1-14 | Received 05 Mar 2023, Accepted 30 Jul 2023, Published online: 03 Oct 2023

References

  • Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton, FL: Chapman and Hall/CRC Press.
  • Banesh, D., Panda, N., Biswas, A., Roekel, L. V., Oyen, D., Urban, N., Grosskopf, M., Wolfe, J., and Lawrence, E. (2021). “Fast Gaussian Process Estimation for Large-Scale in Situ Inference Using Convolutional Neural Networks,” in IEEE International Conference on Big Data, pp. 3731–3739.
  • 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.
  • Bevilacqua, M., Gaetan, C., Mateu, J., and Porcu, E. (2012), “Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach,” Journal of the American Statistical Association, 107, 268–280. DOI: 10.1080/01621459.2011.646928.
  • Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B. (2017), “Julia: A Fresh Approach to Numerical Computing,” SIAM Review, 59, 65–98. DOI: 10.1137/141000671.
  • Casella, G., and Berger, R. (2001), Statistical Inference (2nd ed.), Belmont, CA: Duxbury.
  • Castruccio, S., Huser, R., and Genton, M. G. (2016), “High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes,” Journal of Computational and Graphical Statistics, 25, 1212–1229. DOI: 10.1080/10618600.2015.1086656.
  • Chan, J., Perrone, V., Spence, J., Jenkins, P., Mathieson, S., and Song, Y. (2018), “A Likelihood-Free Inference Framework for Population Genetic Data Using Exchangeable Neural Networks,” in Advances in Neural Information Processing Systems (Vol. 31), eds. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, Curran Associates, Inc.
  • Chon, K., and Cohen, R. (1997), “Linear and Nonlinear ARMA Model Parameter Estimation Using an Artificial Neural Network,” IEEE Transactions on Biomedical Engineering, 44, 168–174. DOI: 10.1109/10.554763.
  • Cox, D., and Reid, N. (2004), “A Note on Pseudolikelihood Constructed from Marginal Densities,” Biometrika, 3, 729–737. DOI: 10.1093/biomet/91.3.729.
  • Creel, M. (2017), “Neural Nets for Indirect Inference,” Econometrics and Statistics, 2, 36–49. DOI: 10.1016/j.ecosta.2016.11.008.
  • Cressie, N. (1993), Statistics for Spatial Data (rev. ed.), Hoboken, NJ: Wiley.
  • ——- (2018), “Mission co2ntrol: A Statistical Scientist’s Role in Remote Sensing of Atmospheric Carbon Dioxide,” Journal of the American Statistical Association, 113, 152–168.
  • ——- (2023), “Decisions, Decisions, Decisions in an Uncertain Environment,” Environmetrics, 34, e2767.
  • Davison, A. C., and Huser, R. (2015), “Statistics of Extremes,” Annual Review of Statistics and its Application, 2, 203–235. DOI: 10.1146/annurev-statistics-010814-020133.
  • Davison, A. C., Huser, R., and Thibaud, E. (2019), “Spatial Extremes,” in Handbook of Environmental and Ecological Statistics, eds. A. E. Gelfand, M. Fuentes, J. A. Hoeting, and R. L. Smith, pp. 711–744, Boca Raton, FL: Chapman & Hall/CRC Press.
  • Diggle, P. J., and Gratton, R. J. (1984), “Monte Carlo Methods of Inference for Implicit Statistical Models,” Journal of the Royal Statistical Society, Series B, 46, 193–227. DOI: 10.1111/j.2517-6161.1984.tb01290.x.
  • Diggle, P. J., and Ribeiro, P. J. (2007), Model-Based Geostatistics, New York, NY: Springer.
  • Donlon, C. J., Martin, M., Stark, J., Roberts-Jones, J., Fiedler, E., and Wimmer, W. (2012), “The Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) System,” Remote Sensing of Environment, 116, 140–158. DOI: 10.1016/j.rse.2010.10.017.
  • Flagel, L., Brandvain, Y., and Schrider, D. R. (2018), “The Unreasonable Effectiveness of Convolutional Neural Networks in Population Genetic Inference,” Molecular Biology and Evolution, 36, 220–238. DOI: 10.1093/molbev/msy224.
  • Gaskin, T., Pavliotis, G. A., and Girolami, M. (2023), “Neural Parameter Calibration for Large-Scale Multiagent Models,” Proceedings of the National Academy of Sciences, 120, e2216415120. DOI: 10.1073/pnas.2216415120.
  • Gerber, F., and Nychka, D. W. (2021), “Fast Covariance Parameter Estimation of Spatial Gaussian Process Models Using Neural Networks,” Stat, 10, e382. DOI: 10.1002/sta4.382.
  • Goodfellow, I., Bengio, Y., and Courville, A. (2016), Deep Learning, Cambridge, MA: MIT Press.
  • Han, J., Li, Y., Lin, L., Lu, J., Zhang, J., and Zhang, L. (2022), “Universal Approximation of Symmetric and Anti-Symmetric Functions,” Communications in Mathematical Sciences, 20, 1397–1408. DOI: 10.4310/CMS.2022.v20.n5.a8.
  • Hazra, A., and Huser, R. (2021), “Estimating High-Resolution Red Sea Surface Temperature Hotspots, Using a Low-Rank Semiparametric Spatial Model,” Annals of Applied Statistics, 15, 572–596.
  • Heffernan, J. E., and Tawn, J. A. (2004), “A Conditional Approach for Multivariate Extreme Values,” Journal of the Royal Statistical Society, Series B, 66, 497–546. DOI: 10.1111/j.1467-9868.2004.02050.x.
  • Hornik, K., Stinchcombe, M., and White, H. (1989), “Multilayer Feedforward Networks are Universal Approximators,” Neural Networks, 2, 359–366. DOI: 10.1016/0893-6080(89)90020-8.
  • Huser, R. (2021), “Editorial: EVA 2019 Data Competition on Spatio-Temporal Prediction of Red Sea Surface Temperature Extremes,” Extremes, 24, 91–104. DOI: 10.1007/s10687-019-00369-9.
  • Huser, R., and Davison, A. C. (2013), “Composite Likelihood Estimation for the Brown–Resnick Process,” Biometrika, 100, 511–518. DOI: 10.1093/biomet/ass089.
  • Huser, R., Dombry, C., Ribatet, M., and Genton, M. G. (2019), “Full Likelihood Inference for Max-Stable Data,” Stat, 8, e218. DOI: 10.1002/sta4.218.
  • Huser, R., Stein, M. L., and Zhong, P. (2022), “Vecchia Likelihood Approximation for Accurate and Fast Inference in Intractable Spatial Extremes Models,” arXiv:2203.05626v1.
  • Huser, R., and Wadsworth, J. (2022), “Advances in Statistical Modeling of Spatial Extremes,” Wiley Interdisciplinary Reviews: Computational Statistics, 14, e1537.
  • Innes, M. (2018), “Flux: Elegant Machine Learning with Julia,” Journal of Open Source Software, 3, 602. DOI: 10.21105/joss.00602.
  • Lehmann, E. L., and Casella, G. (1998), Theory of Point Estimation (2nd ed.), New York: Springer.
  • Lenzi, A., Bessac, J., Rudi, J., and Stein, M. L. (2023), “Neural Networks for Parameter Estimation in Intractable Models,” Computational Statistics & Data Analysis, 185, 107762. DOI: 10.1016/j.csda.2023.107762.
  • Lintusaari, J., Gutmann, M., Dutta, R., Kaski, S., and Corander, J. (2017), “Fundamentals and Recent Developments in Approximate Bayesian Computation,” Systematic Biology, 66, 66–82. DOI: 10.1093/sysbio/syw077.
  • McCullagh, P. (2002), “What is a Statistical Model,” The Annals of Statistics, 30, 1225–1310. DOI: 10.1214/aos/1035844977.
  • Murphy, R. L., Srinivasan, B., Rao, V. A., and Ribeiro, B. (2019), “Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs,” in 7th International Conference on Learning Representations, ICLR.
  • Pacchiardi, L., and Dutta, R. (2022), “Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimization,” arXiv:2205.15784.
  • Padoan, S. A., Ribatet, M., and Sisson, S. A. (2010), “Likelihood-based Inference for Max-Stable Processes,” Journal of the American Statistical Association, 105, 263–277. DOI: 10.1198/jasa.2009.tm08577.
  • Radev, S. T., Mertens, U. K., Voss, A., Ardizzone, L., and Köthe, U. (2022), “BayesFlow: Learning Complex Stochastic Models with Invertible Neural Networks,” IEEE Transactions on Neural Networks and Learning Systems, 33, 1452–1466. DOI: 10.1109/TNNLS.2020.3042395.
  • R Core Team. (2023), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Richards, J., Tawn, J. A., and Brown, S. (2022), “Modelling Extremes of Spatial Aggregates of Precipitation Using Conditional Methods,” Annals of Applied Statistics, 16, 2693–2713.
  • Rudi, J., Julie, B., and Lenzi, A. (2021), “Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODE,” in Proceedings of the 2nd Annual Conference on Mathematical and Scientific Machine Learning, volume 145 of Proceedings of Machine Learning Research, eds. J. Bruna, J. Hesthaven, and L. Zdeborova, pp. 1–28, PMLR.
  • Sang, H., and Genton, M. G. (2012), “Tapered Composite Likelihood for Spatial Max-Stable Models,” Spatial Statistics, 8, 86–103. DOI: 10.1016/j.spasta.2013.07.003.
  • Schlather, M. (2002), “Models for Stationary Max-Stable Random Fields,” Extremes, 5, 33–44.
  • Simpson, E. S., Opitz, T., and Wadsworth, J. L. (2023), “High-Dimensional Modeling of Spatial and Spatio-Temporal Conditional Extremes Using INLA and Gaussian Markov Random Fields,” Extremes, to appear. DOI: 10.1007/s10687-023-00468-8.
  • Simpson, E. S., and Wadsworth, J. L. (2021), “Conditional Modelling of Spatio-Temporal Extremes for Red Sea Surface Temperatures,” Spatial Statistics, 41, 100482. DOI: 10.1016/j.spasta.2020.100482.
  • Sisson, S. A., Fan, Y., and Beaumont, M. (2018), Handbook of Approximate Bayesian Computation, Boca Raton, FL: Chapman & Hall/CRC Press.
  • Soelch, M., Akhundov, A., van der Smagt, P., and Bayer, J. (2019), “On Deep Set Learning and the Choice of Aggregations,” in Proceedings of the 28th International Conference on Artificial Neural Networks, ICANN, Lecture Notes in Computer Science, eds. I. V. Tetko, V. Kurková, P. Karpov, and F. J. Theis, pp. 444–457, Springer.
  • Stein, M. L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer.
  • Stein, M. L., Chi, Z., and Welty, L. J. (2004), “Approximating Likelihoods for Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series, B, 66, 275–296. DOI: 10.1046/j.1369-7412.2003.05512.x.
  • Strasser, H. (1981), “Consistency of Maximum Likelihood and Bayes Estimates,” The Annals of Statistics, 9, 1107–1113. DOI: 10.1214/aos/1176345590.
  • Subbotin, M. T. (1923), “On the Law of Frequency of Errors,” Mathematicheskii Sbornik, 31, 296–301.
  • Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
  • Varin, C., and Vidoni, P. (2005), “A Note on Composite Likelihood Inference and Model Selection,” Biometrika, 92, 519–528. DOI: 10.1093/biomet/92.3.519.
  • Vecchia, A. V. (1988), “Estimation and Model Identification for Continuous Spatial Processes,” Journal of the Royal Statistical Society, Series B, 50, 297–312. DOI: 10.1111/j.2517-6161.1988.tb01729.x.
  • Wadsworth, J. L., and Tawn, J. A. (2022), “Higher-Dimensional Spatial Extremes via Single-Site Conditioning,” Spatial Statistics, 51, 100677. DOI: 10.1016/j.spasta.2022.100677.
  • Wagstaff, E., Fuchs, F. B., Engelcke, M., Osborne, M., and Posner, I. (2022), “Universal Approximation of Functions on Sets,” Journal of Machine Learning Research, 23, 1–56.
  • Wagstaff, E., Fuchs, F. B., Engelcke, M., Posner, I., and Osborne, M. (2019), “On the Limitations of Representing Functions on Sets,” in Proceedings of the 36th International Conference on Machine Learning (Vol. 97), eds. K. Chaudhuri and R. Salakhutdinov, pp. 6487–6494, PMLR.
  • Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., and Yu, P. S. (2021), “A Comprehensive Survey on Graph Neural Networks,” IEEE Transactions on Neural Networks and Learning Systems, 32, 4–24. DOI: 10.1109/TNNLS.2020.2978386.
  • Zaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R. R., and Smola, A. J. (2017), “Deep Sets,” in Advances in Neural Information Processing Systems (Vol. 30), eds. I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, Curran Associates, Inc.
  • Zammit-Mangion, A., and Wikle, C. K. (2020), “Deep Integro-Difference Equation Models for Spatio-Temporal Forecasting,” Spatial Statistics, 37, 100408. DOI: 10.1016/j.spasta.2020.100408.
  • Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-based Geostatistics,” Journal of the American Statistical Association, 99, 250–261. DOI: 10.1198/016214504000000241.
  • Zhou, D. (2018), “Universality of Deep Convolutional Neural Networks,” Applied and Computational Harmonic Analysis, 48, 787–794. DOI: 10.1016/j.acha.2019.06.004.