765
Views
2
CrossRef citations to date
0
Altmetric
Research Articles

Model Mixing Using Bayesian Additive Regression Trees

, , & ORCID Icon
Pages 196-207 | Received 16 Dec 2022, Accepted 06 Sep 2023, Published online: 18 Oct 2023

References

  • Bernardo, J. M., and Smith, A. F. (1994), Bayesian Theory, Chichester: Wiley.
  • Breiman, L. (1996), “Stacked Regressions,” Machine Learning, 24, 49–64. DOI: 10.1007/BF00117832.
  • Bunea, F., Tsybakov, A. B., and Wegkamp, M. H. (2007), “Aggregation for Gaussian Regression,” The Annals of Statistics, 35, 1674–1697. DOI: 10.1214/009053606000001587.
  • Burgess, C. P. (2020), Introduction to Effective Field Theory: Thinking Effectively about Hierarchies of Scale, Cambridge: Cambridge University Press.
  • Burnham, K. P., and Anderson, D. R. (1998), “Practical Use of the Information-Theoretic Approach,” in Model Selection and Inference, pp. 75–117, New York: Springer.
  • Chipman, H. A., George, E. I., and McCulloch, R. E. (1998), “Bayesian CART Model Search,” Journal of the American Statistical Association, 93, 935–948. DOI: 10.1080/01621459.1998.10473750.
  • ———(2002), “Bayesian Treed Models,” Machine Learning, 48, 299–320.
  • Chipman, H., George, E., and McCulloch, R. (2010), “BART: Bayesian Additive Regression Trees,” The Annals of Applied Statistics, 4, 266–298. DOI: 10.1214/09-AOAS285.
  • Clyde, M., and Iversen, E. S. (2013), “Bayesian Model Averaging in the M-Open Framework,” in Bayesian Theory and Applications, eds. P. Damien, P. Dellaportas, N. G. Polson, and D. A. Stephens, 484–498, Oxford: Oxford University Press.
  • Draper, D. (1995), “Assessment and Propagation of Model Uncertainty,” Journal of the Royal Statistical Society, Series B, 57, 45–70. DOI: 10.1111/j.2517-6161.1995.tb02015.x.
  • Georgi, H. (1993), “Effective Field Theory,” Annual Review of Nuclear and Particle Science, 43, 209–252. DOI: 10.1146/annurev.ns.43.120193.001233.
  • Gramacy, R. B. (2020), Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences, Boca Raton, FL: Chapman and Hall/CRC.
  • Gramacy, R. B., and Lee, H. K. H. (2008), “Bayesian Treed Gaussian Process Models with an Application to Computer Modeling,” Journal of the American Statistical Association, 103, 1119–1130. DOI: 10.1198/016214508000000689.
  • Hansen, B. E. (2007), “Least Squares Model Averaging,” Econometrica, 75, 1175–1189. DOI: 10.1111/j.1468-0262.2007.00785.x.
  • Hastie, T., and Tibshirani, R. (2000), “Bayesian Backfitting” (with comments and a rejoinder), Statistical Science, 15, 196–223. DOI: 10.1214/ss/1009212815.
  • Honda, M. (2014), “On Perturbation Theory Improved by Strong Coupling Expansion,” Journal of High Energy Physics, 2014, 1–44. DOI: 10.1007/JHEP12(2014)019.
  • Le, T., and Clarke, B. (2017), “A Bayes Interpretation of Stacking for M-complete and M-open Settings,” Bayesian Analysis, 12, 807–829. DOI: 10.1214/16-BA1023.
  • Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., and Wesolowski, S. (2019), “Quantifying Correlated Truncation Errors in Effective Field Theory,” Physical Review C, 100, 044001. DOI: 10.1103/PhysRevC.100.044001.
  • Melendez, J., Furnstahl, R., Grießhammer, H., McGovern, J., Phillips, D., and Pratola, M. (2021), “Designing Optimal Experiments: An Application to Proton Compton Scattering,” The European Physical Journal A, 57, 1–24. DOI: 10.1140/epja/s10050-021-00382-2.
  • Petrov, A. A., and Blechman, A. E. (2016), Effective Field Theories, Singapore: World Scientific. https://www.worldscientific.com/doi/abs/10.1142/8619
  • Phillips, D., Furnstahl, R., Heinz, U., Maiti, T., Nazarewicz, W., Nunes, F., Plumlee, M., Pratola, M., Pratt, S., Viens, F. et al. (2021), “Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics,” Journal of Physics G: Nuclear and Particle Physics, 48, 072001. DOI: 10.1088/1361-6471/abf1df.
  • Prado, E. B., Moral, R. A., and Parnell, A. C. (2021), “Bayesian Additive Regression Trees with Model Trees,” Statistics and Computing, 31, 1–13. DOI: 10.1007/s11222-021-09997-3.
  • Pratola, M. T. (2016), “Efficient Metropolis–Hastings Proposal Mechanisms for Bayesian Regression Tree Models,” Bayesian Analysis, 11, 885–911. DOI: 10.1214/16-BA999.
  • Raftery, A., Madigan, D., and Hoeting, J. (1997), “Bayesian Model Averaging for Linear Regression Models,” Journal of the American Statistical Association, 92, 179–191. DOI: 10.1080/01621459.1997.10473615.
  • Santner, T. J., Williams, B. J., and Notz, W. I. (2018), The Design and Analysis of Computer Experiments (2nd ed.), New York: Springer.
  • Semposki, A. C., Furnstahl, R. J., and Phillips, D. R. (2022), “Interpolating Between Small- and Large-g Expansions Using Bayesian Model Mixing,” Physical Review C, 106, 044002. DOI: 10.1103/PhysRevC.106.044002.
  • Sill, J., Takács, G., Mackey, L., and Lin, D. (2009), “Feature-Weighted Linear Stacking,” arXiv preprint arXiv:0911.0460 .
  • Yang, Y., and Dunson, D. B. (2014), “Minimax Optimal Bayesian Aggregation,” arXiv preprint arXiv:1403.1345.
  • Yao, Y., Pirš, G., Vehtari, A., and Gelman, A. (2021), “Bayesian Hierarchical Stacking: Some Models are (somewhere) Useful,” Bayesian Analysis, 1, 1–29. DOI: 10.1214/21-BA1287.
  • Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018), “Using Stacking to Average Bayesian Predictive Distributions,” Bayesian Analysis, 13, 917–1007. DOI: 10.1214/17-BA1091.