ABC of the future. (English) Zbl 07779067
Summary: Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The computational feasibility of ABC for practical applications has been recently boosted by adopting techniques from machine learning to build surrogate models for the approximate likelihood or posterior and by the introduction of a general-purpose software platform with several advanced features, including automated parallelisation. Here we demonstrate the strengths of the advances in ABC by going beyond the typical benchmark examples and considering real applications in astronomy, infectious disease epidemiology, personalised cancer therapy and financial prediction. We anticipate that the emerging success of ABC in producing actual added value and quantitative insights in the real world will continue to inspire a plethora of further applications across different fields of science, social science and technology.
© 2022 The Authors. International Statistical Review published by John Wiley & Sons Ltd on behalf of International Statistical Institute.
© 2022 The Authors. International Statistical Review published by John Wiley & Sons Ltd on behalf of International Statistical Institute.
Keywords:
approximate Bayesian computation; Bayesian inference; likelihood-free inference; simulator-based inferenceReferences:
| [1] | Alarcón, T., Byrne, H.M. & Maini, P.K. (2010). A multiple scale model for tumor growth. Multiscale Model. Simul., 3(2), 440. · Zbl 1107.92019 |
| [2] | Althaus, C.L. (2014). Estimating the reproduction number of ebola virus (ebov) during the 2014 outbreak in west africa. PLoS currents, 6. |
| [3] | An, Z., South, L.F. & Drovandi, C.2019. BSL: An R Package for Efficient Parameter Estimation for Simulation‐Based Models via Bayesian Synthetic Likelihood. arXiv preprint 1907.10940. |
| [4] | An, Z., South, L.F., Nott, D.J. & Drovandi, C.C. (2019). Accelerating Bayesian synthetic likelihood with the graphical lasso. J. Comput. Graph. Stat., 28(2), 471-475. · Zbl 07499068 |
| [5] | Andrieu, C. & Doucet, A. (2010). Particle Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. B, 72, 263-342. · Zbl 1411.65020 |
| [6] | Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian J. Stat., 12(2) 171-178. · Zbl 0581.62014 |
| [7] | Beaumont, M.A. (2019). Approximate Bayesian Computation. Ann. Rev. Stat. Appl., 6(1), 379-403. https://doi.org/10.1146/annurev‐statistics‐030718‐105212 · doi:10.1146/annurev‐statistics‐030718‐105212 |
| [8] | Beaumont, M.A., Cornuet, J.‐M., Marin, J.‐M. & Robert, C.P. (2009). Adaptive approximate Bayesian computation. Biometrika, 96(4), 983-990. · Zbl 1437.62393 |
| [9] | Billio, M., Casarin, R., Ravazzola, F. & vanDijk, H.K. (2013). Time‐varying combinations of predictive densities using nonlinear filtering. J. Econ., 177, 213-232. · Zbl 1288.62136 |
| [10] | Blum, M.G.B. (2010). Approximate Bayesian computation: A nonparametric perspective. J. Am. Stat. Assoc., 105(491), 1178-1187. · Zbl 1390.62052 |
| [11] | Britton, T. & Tomba, G.S. (2019). Estimation in emerging epidemics: Biases and remedies. J. R. Soc. Interface, 16(150), 20180670. |
| [12] | Brochu, E., Cora, V.M. & de Freitas, N.2010. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:1012.2599. |
| [13] | Brooks, C. (2014). Introductory Econometrics for Finance. Cambridge University Press. · Zbl 1141.91001 |
| [14] | Cameron, E. & Pettitt, A.N. (2012). Approximate bayesian computation for astronomical model analysis: A case study in galaxy demographics and morphological transformation at high redshift. Monthly Notices R. Astronomical Soc., 425, 44-65. |
| [15] | Chinazzi, M., Davis, J.T., Ajelli, M., Gioannini, C., Litvinova, M., Merler, S., Pastore y Piontti, A., Mu, K., Rossi, L., Sun, K., Viboud, C., Xiong, X., Yu, H., Halloran, M.E., Longini, I.M. & Vespignani, A. (2020). The effect of travel restrictions on the spread of the 2019 novel coronavirus (covid‐19) outbreak. Science, 368(6489), 395-400. https://science.sciencemag.org/content/368/6489/395.full.pdf |
| [16] | Cisewski‐Kehe, J., Weller, G., Schafer, C. et al. (2019). A preferential attachment model for the stellar initial mass function. Electronic J. Stat., 13(1), 1580-1607. · Zbl 1423.85006 |
| [17] | Clarté, G., Robert, C.P., Ryder, R.J. & Stoehr, J. (2021). Componentwise approximate Bayesian computation via Gibbs‐like steps. Biometrika, 108(3), 591-607. https://academic.oup.com/biomet/advance‐article‐pdf/doi/10.1093/biomet/asaa090/36332711/asaa090.pdf · Zbl 07459718 |
| [18] | Corander, J., Fraser, C., Gutmann, M.U., Arnold, B., Hanage, W.P., Bentley, S.D., Lipsitch, M. & Croucher, N.J. (2017). Frequency‐dependent selection in vaccine‐associated pneumococcal population dynamics. Narure Ecology Evol., 1(12), 1950-1960. |
| [19] | Cranmer, K., Brehmer, J. & Louppe, G. (2020). The frontier of simulation‐based inference. Proc. Nat. Acad. Sci., 117(48), 30055-30062. https://www.pnas.org/content/117/48/30055.full.pdf · Zbl 1485.62004 |
| [20] | Csilléry, K., Blum, M.G.B., Gaggiotti, O.E. & François, O. (2010). Approximate Bayesian computation (ABC) in practice. Trends Ecology Evol., 25(7), 410-418. |
| [21] | Depeweg, S., Hernández‐Lobato, J.M., Doshi‐Velez, F. & Udluft, S.2017. Decomposition of uncertainty in bayesian deep learning for efficient and risk‐sensitive learning. arXiv preprint arXiv:1710.07283. |
| [22] | Drovandi, C.C. & Pettitt, A.N. (2011). Estimation of parameters for macroparasite population evolution using approximate bayesian computation. biometrics. Stat. Comput., 67(1), 225-233. · Zbl 1217.62128 |
| [23] | Drovandi, C.C., Pettitt, A.N. & Faddy, M.J. (2011). Approximate bayesian computation using indirect inference. J. R. Stat. Soc. Ser. C, 60, 1-21. |
| [24] | Drovandi, C.C., Pettitt, A.N. & Lee, A. (2015). Bayesian indirect inference using a parametric auxiliary model. Stat. Sci., 30, 72-95. · Zbl 1332.62088 |
| [25] | Dutta, R., Schoengens, M., Onnela, J.‐P. & Mira, A. (2017). Abcpy: A user‐friendly, extensible, and parallel library for approximate Bayesian computation. In Proceedings of the Platform for Advanced Scientific Computing Conference, PASC ’17, pp. 8:1-8:9. ACM, Association for Computing Machinery: New York, NY, USA. |
| [26] | Ebert, A., Dutta, R., Mengersen, K., Mira, A., Ruggeri, F. & Wu, P. (2021). Likelihood‐free parameter estimation for dynamic queueing networks: Case study of passenger flow in an international airport terminal. J. R. Stat. Soc.: Ser. C (Appl. Stat.), 70(3), 770-792. https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/rssc.12487 |
| [27] | Fearnhead, P. & Prangle, D. (2012). Constructing summary statistics for approximate bayesian computation: semi‐automatic approximate bayesian computation. J. R. Stat. Soc.: Ser. B (Stat. Methodol.), 74(3), 419-474. https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467‐9868.2011.01010.x · Zbl 1411.62057 |
| [28] | Forbes, F., Nguyen, H.D., Nguyen, T.T. & Arbel, J.2021. Approximate Bayesian computation with surrogate posteriors. working paper or preprint. |
| [29] | Frazier, D.T., Maneesoonthorn, W., Martin, G.M. & McCabe, B.P.M. (2019). Approximate Bayesian forecasting. Int. J. Forecast., 35(2), 521-539. |
| [30] | Frazier, D.T., Martin, G.M., Robert, C.P. & Rousseau, J. (2018). Asymptotic properties of approximate bayesian computation. Biometrika, 105, 593-607. · Zbl 1499.62112 |
| [31] | Frazier, D.T., Robert, C.P. & Rousseau, J. (2020). Model misspecification in approximate Bayesian computation: consequences and diagnostics. J. R. Stat. Soc. Ser. B, 82(2), 421-444. · Zbl 07554760 |
| [32] | Gal, Y., Islam, R. & Ghahramani, Z.2017. Deep Bayesian active learning with image data. arXiv preprint arXiv:1703.02910. |
| [33] | Gebhardt, C., Oulasvirta, A. & Hilliges, O. (2020). Hierarchical reinforcement learning explains task interleaving behavior. Comput. Brain Behavior, 4(3), 284-304. |
| [34] | Grazian, C. & Fan, Y. (2020). A review of approximate Bayesian computation methods via density estimation: Inference for simulator‐models. WIREs Comput. Stat., 12(4), e1486. https://onlinelibrary.wiley.com/doi/pdf/10.1002/wics.1486 · Zbl 07909794 |
| [35] | Green, P.J., Łatuszyński, K., Pereyra, M. & Robert, C.P. (2015). Bayesian computation: A summary of the current state, and samples backwards and forwards. Stat. Comput., 25(4), 835-862. · Zbl 1331.62017 |
| [36] | Gutmann, M.U. & Corander, J. (2016). Bayesian optimization for likelihood‐free inference of simulator‐based statistical models. J. Machine Learn. Res., 17(125), 1-47. · Zbl 1392.62072 |
| [37] | Gutmann, M.U., Dutta, R., Kaski, S. & Corander, J. (2018). Likelihood‐free inference via classification. Stat. Comput., 28(2), 411-425. · Zbl 1384.62089 |
| [38] | Guy, J., Sullivan, M., Conley, A., Regnault, N., Astier, P., Balland, C., Basa, S., Carlberg, R.G., Fouchez, D., Hardin, D. & Hook, I.M. (2010). The supernova legacy survey 3‐year sample: Type ia supernovae photometric distances and cosmological constraints. Astron. Astrophys., 523, A7. |
| [39] | Hinton, S.R., Davis, T.M., Kim, A.G., Brout, D., D’Andrea, C.B., Kessler, R., Lasker, J., Lidman, C., Macaulay, E., Möller, A. & Sako, M. (2019). Steve: A hierarchical Bayesian model for supernova cosmology. Astrophys. J., 876(1), 15. |
| [40] | Hoffman, M.D. & Gelman, A. (2014). The no‐u‐turn sampler: Adaptively setting path lengths in hamiltonian monte carlo. J. Machine Learn. Res., 15(47), 1593-1623. · Zbl 1319.60150 |
| [41] | Houlsby, N., Huszár, F., Ghahramani, Z. & Lengyel, M.2011. Bayesian Active Learning for Classification and Preference Learning. arXiv preprint arXiv:1112.5745. |
| [42] | Ishida, E.E.O., Vitenti, S.D.P., Penna‐Lima, M., Cisewski, J., de Souza, R.S., Trindade, A.M.M., Cameron, E. & Busti, V.C. (2015). cosmoabc: Likelihood‐free inference via population monte carlo approximate Bayesian computation. Astron. Comput., 13, 1-11. |
| [43] | Järvenpää, M., Gutmann, M.U., Pleska, A., Vehtari, A. & Marttinen, P. (2019). Efficient Acquisition Rules for Model‐Based Approximate Bayesian Computation. Bayesian Anal., 14(2), 595-622. · Zbl 1416.62453 |
| [44] | Jennings, E. & Madigan, M. (2017). astroabc: An approximate bayesian computation sequential monte carlo sampler for cosmological parameter estimation. Astron. Comput., 19, 16-22. |
| [45] | Joyce, P. & Marjoram, P. (2008). Approximately sufficient statistics and Bayesian computation. Stat. Appl. Gen. Molec. Biol., 7(1), 1-16. · Zbl 1276.62077 |
| [46] | Kangasrääsiö, A., Athukorala, K., Howes, A., Corander, J., Kaski, S. & Oulasvirta, A. (2017). Inferring cognitive models from data using approximate bayesian computation. In Proceedings of the 2017 chi conference on human factors in computing systems, CHI’17, pp. 1295-1306. Association for Computing Machinery, Association for Computing Machinery: New York, NY, USA. |
| [47] | Kangasrääsiö, A., Jokinen, J.P.P., Oulasvirta, A., Howes, A. & Kaski, S. (2019). Parameter inference for computational cognitive models with approximate Bayesian computation. Cognitive Sci., 43(6), e12738. https://onlinelibrary.wiley.com/doi/pdf/10.1111/cogs.12738 |
| [48] | Kessler, R., Bernstein, J.P., Cinabro, D., Dilday, B., Frieman, J.A., Jha, S., Kuhlmann, S., Miknaitis, G., Sako, M., Taylor, M. & Vanderplas, J (2009). Snana: A public software package for supernova analysis. Publications Astron. Soc. Pacific, 121(883), 1028. |
| [49] | Kessler, R., Guy, J., Marriner, J., Betoule, M., Brinkmann, J., Cinabro, D., El‐Hage, P., Frieman, J.A., Jha, S., Mosher, J. & Schneider, D.P. (2013). Testing models of intrinsic brightness variations in type ia supernovae and their impact on measuring cosmological parameters. Astrophys. J., 764(1), 48. |
| [50] | Kokko, J., Remes, U., Thomas, O., Pesonen, H. & Corander, J. (2019). Pylfire: Python implementation of likelihood‐free inference by ratio estimation. Wellcome Open Res., 4. |
| [51] | Kozłowska, E., Färkkilä, A., Vallius, T., Carpén, O., Kemppainen, J., Grénman, S., Lehtonen, R., Hynninen, J., Hietanen, S. & Hautaniemi, S. (2018). Mathematical modeling predicts response to chemotherapy and drug combinations in ovarian cancer. Cancer Res., 78(14), 4036-4044. https://cancerres.aacrjournals.org/content/78/14/4036.full.pdf |
| [52] | Lai, X., Geier, O., Fleischer, T., Garred, O., Borgen, E.F., Funke, S., Kumar, S., Rognes, M.E., Seierstad, T., Boerresen‐Dale, A.‐L., Kristensen, V.N., Engebraaten, O., Köhn‐Luque, A. & Frigessi, A. (2019). Towards personalized computer simulation of breast cancer treatment: A multi‐scale pharmacokinetic and pharmacodynamic model informed by multi‐type patient data. Cancer Res., 73, 41-49. |
| [53] | Lai, X., Taskén, H.A., Mo, T., Funke, S.W., Frigessi, A., Rognes, M.E. & Köhn‐Luque, A. (2021). A scalable solver for a stochastic, hybrid cellular automaton model of personalized breast cancer therapy. Int. J. Numer. Methods Biomed. Eng., 38(1), e3542. https://onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.3542 |
| [54] | Leclercq, F. (2018). Bayesian optimization for likelihood‐free cosmological inference. Phys. Rev. D, 98(6), 63511. |
| [55] | Lenormand, M., Jabot, F. & Deuant, G. (2013). Adaptive approximate bayesian computation for complex models. Comput. Stat., 6(28), 2777-2796. · Zbl 1306.65088 |
| [56] | Li, W. & Fearnhead, P. (2018a). Convergence of regression‐adjusted approximate Bayesian computation. Biometrika, 105(2), 301-318. · Zbl 07072414 |
| [57] | Li, W. & Fearnhead, P. (2018b). On the asymptotic efficiency of approximate Bayesian computation estimators. Biometrika, 105(2), 285-299. · Zbl 07072413 |
| [58] | Lintusaari, J., Blomstedt, P., Rose, B., Sivula, T., Gutmann, M.U., Kaski, S. & Corander, J. (2019). Resolving outbreak dynamics using Approximate Bayesian Computation for stochastic birth‐death models [version 2; peer review: 2 approved]. Wellcome Open Res, 4(14). |
| [59] | Lintusaari, J., Gutmann, M.U., Dutta, R., Kaski, S. & Corander, J. (2017). Fundamentals and Recent Developments in Approximate Bayesian Computation. System. Biol., 66, 66-82. |
| [60] | Lintusaari, J., Vuollekoski, H., Kangasrääsiö, A., Skytén, K., Järvenpää, M., Marttinen, P., Gutmann, M.U., Vehtari, A., Corander, J. & Kaski, S. (2018). ELFI: Engine for Likelihood‐Free Inference. J. Machine Learn. Res., 19(16), 1-7. |
| [61] | Lueckmann, J.‐M., Bassetto, G., Karaletsos, T. & Macke, J.H.2018. Likelihood‐free inference with emulator networks. arXiv preprint arXiv:1805.09294. |
| [62] | Marin, J.‐M., Pillai, N.S., Robert, C.P. & Rousseau, J. (2014). Relevant statistics for Bayesian model choice. J. R. Stat. Soc.: Ser. B (Stat. Methodol.), 76, 833-859. · Zbl 1411.62072 |
| [63] | Marin, J.‐M., Pudlo, P., Robert, C.P. & Ryder, R.J. (2012). Approximate Bayesian computational methods. Stat. Comput., 22, 1167-1180. · Zbl 1252.62022 |
| [64] | Marjoram, P. (2013). Approximate Bayesian Computation. OA Gen., 1, 853. |
| [65] | Marjoram, P., Molitor, J., Plagnol, V. & Tavare, S. (2003). Markov chain Monte Carlo without likelihoods. Proc. Nat. Acad. Sci. United States Am., 100, 15324-15328. |
| [66] | Martin, G.M., McCabe, B.rendanP.M., Frazier, D.T., Maneesoonthorn, W. & Robert, C.P. (2019). Auxiliary likelihood‐based approximate Bayesian computation in state space models. J. Comput. Graph. Stat., 28(3), 508-522. · Zbl 07499073 |
| [67] | McKinley, T., Cook, A.R. & Deardon, R. (2009). Inference in epidemic models without likelihoods. Int. J. Biostat., 5(1), 1-37. |
| [68] | Moral, P.D., Doucet, A. & Jasra, A. (2012). An adaptive sequential Monte Carlo method for approximate Bayesian computation. Stat. Comput., 22(5), 1009-1020. · Zbl 1252.65025 |
| [69] | Ong, V.M.‐H., Nott, D.J., Tran, M.‐N., Sisson, S.A. & Drovandi, C.C. (2018). Likelihood‐free inference in high dimensions with synthetic likelihood. Comput. Stat. Data Anal., 128, 271-291. · Zbl 1469.62123 |
| [70] | Papamakarios, G., Sterratt, D.C. & Murray, I. (2019). Sequential neural likelihood: Fast likelihood‐free inference with autoregressive flows. In Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, Vol. 89, pp. 837-848. PMLR, Society for Artificial Intelligence and Statistics. |
| [71] | Picchini, U., Simola, U. & Corander, J.2020. Adaptive mcmc for synthetic likelihoods and correlated synthetic likelihoods. arXiv preprint arXiv:2004.04558. |
| [72] | Prangle, D. (2017). Adapting the ABC Distance Function. Bayesian Anal., 12, 289-309. · Zbl 1384.62098 |
| [73] | Price, L.F., Drovandi, C.C., Lee, A. & Nott, D.J. (2018). Bayesian synthetic likelihood. J. Comput. Graph. Stat., 27(1), 1-11. · Zbl 07498962 |
| [74] | Pritchard, J.K., Seielstad, M.T., Perez‐Lezaun, A. & Feldman, M.W. (1999). Population growth of human Y chromosomes: a study of Y chromosome microsatellites.Molec. Biol. Evol., 16(12), 1791-1798. |
| [75] | Rasmussen, C.E. & Williams, K.I. (2006). Gaussian processes for machine learning. MIT Press. · Zbl 1177.68165 |
| [76] | Ribba, B., Alarcón, T., Marron, K., Maini, P.K. & Agur, Z. (2004). The use of hybrid cellular automaton models for improving cancer therapy. In International Conference on Cellular Automata, pp. 444-453, Springer. · Zbl 1116.92314 |
| [77] | Rodrigues, G.S., Nott, D.J. & Sisson, S.A. (2020). Likelihood‐free approximate Gibbs sampling. Stat. Comput., 30, 1057-1073. · Zbl 1447.62012 |
| [78] | Schafer, C.M. & Freeman, P.E. (2012). Statistical challenges in modern astronomy V, Lecture Notes in Statistics. Springer. |
| [79] | Shen, P., Lees, J.A., Bee, G.C.W., Brown, S.P. & N., W.J. (2019). Pneumococcal quorum sensing drives an asymmetric owner‐intruder competitive strategy during carriage via the competence regulon. Nature Microbiol., 4, 198-208. |
| [80] | Silk, D., Filippi, S. & Stumpf, M.P.H. (2013). Optimizing threshold‐schedules for sequential approximate bayesian computation: Applications to molecular systems. Stat. Appl. Gen. Molecul. Biol., 5(12), 603-618. |
| [81] | Simola, U., Cisewski‐Kehe, J., Gutmann, M.U. & Corander, J. (2020). Adaptive approximate bayesian computation tolerance selection. Bayesian Anal., 16(2), 397-423. · Zbl 1480.62165 |
| [82] | Simola, U., Pelssers, B., Barge, D., Conrad, J. & Corander, J. (2019). Machine learning accelerated likelihood‐free event reconstruction in dark matter direct detection. J. Instrument., 14(3), P03004. |
| [83] | Sisson, S.A., Fan, Y. & Beaumont, M. (2018). Handbook of approximate bayesian computation, Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press, Taylor & Francis Group. |
| [84] | Sottoriva, A. & Tavaré, S. (2010). Integrating approximate Bayesian computation with complex agent‐based models for cancer research. In Proceedings of Compstat’2010, pp. 57-66. Springer. · Zbl 1436.62636 |
| [85] | Srinivas, N., Krause, A., Kakade, S.M. & Seeger, M. (2010). Gaussian process optimization in the bandit setting: No regret and experimental design. In Proceedings of the 27th International Conference on Machine Learning (ICML), Israel, ICML. |
| [86] | Tavaré, S., Balding, D.J., Griffiths, R.C. & Donnelly, P. (1997). Inferring coalescence times from dna sequence data. Genetics, 145(2), 505-518. |
| [87] | Tejero‐Cantero, A., Boelts, J., Deistler, M., Lueckmann, J.‐M., Durkan, C., Gonçalves, P.J., Greenberg, D.S. & Macke, J.H. (2020). SBI: A toolkit for simulation‐based inference. J. Open Source Softw., 5(52), 2505. |
| [88] | Thomas, O., Dutta, R., Corander, J., Kaski, S. & Gutmann, M.U. (2022). Likelihood‐free inference by ratio estimation. Bayesian Anal., 17(1), 1-31. Advance publication. · Zbl 07809841 |
| [89] | Toni, T., Welch, D., Strelkowa, N., Ipsen, A. & Stumpf, M.P.H. (2009). Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interf., 6(31), 187-202. |
| [90] | Vihola, M. & Franks, J. (2020). On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post‐correction. Biometrika, 107, 381-395. · Zbl 1441.62088 |
| [91] | vonNeumann, J. & Morgenstern, O. (1953). Theory of Games and Economic Behavior. Princeton University Press. · Zbl 0053.09303 |
| [92] | WHO Ebola Response Team (2014). Ebola virus disease in West Africa - The first 9 months of the epidemic and forward projections. New England J. Med., 371(16), 1481-1495. |
| [93] | Weyant, A., Schafer, C. & Wood‐Vasey, W.M. (2013). Likelihood‐free cosmological inference with type Ia supernovae: approximate Bayesian computation for a complete treatment of uncertainty. Astrophys. J., 764, 116. |
| [94] | Wood, S.N. (2010). Statistical inference for noisy nonlinear ecological dynamic systems. Nature, 466, 1102-1107. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
