428
Views
1
CrossRef citations to date
0
Altmetric
Articles

Bayesian adaptive selection of basis functions for functional data representation

ORCID Icon, ORCID Icon & ORCID Icon
Pages 958-992 | Received 26 May 2022, Accepted 18 Jan 2023, Published online: 03 Feb 2023

References

  • J. Álvaro, COVID-19: Boletins informativos e casos do coronavírus, (2021). Available at https://brasil.io/dataset/covid19/caso_full/. [Online; accessed 17-August-2021; Licença: Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)].
  • C.A. Anselmo, R. Dias, and N.L. Garcia, Adaptive basis selection for functional data analysis via stochastic penalization, Comput. Appl. Math. 24 (2005), pp. 209–229.
  • D.M. Blei, A. Kucukelbir, and J.D. McAuliffe, Variational inference: A review for statisticians, J. Am. Stat. Assoc. 112 (2017), pp. 859–877.
  • P.J. Brown, M. Vannucci, and T. Fearn, Multivariate Bayesian variable selection and prediction, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 60 (1998), pp. 627–641.
  • X. Cai, L. Xue, J. Cao, and A.D.N. Initiative, Robust estimation and variable selection for function-on-scalar regression, Can. J. Stat. 50 (2022), pp. 162–179.
  • B.P. Carlin and S. Chib, Bayesian model choice via Markov chain Monte Carlo methods, J. R. Stat. Soc. Ser. B (Methodol.) 57 (1995), pp. 473–484.
  • G. Casella and E.I. George, Explaining the Gibbs Sampler, Am. Stat. 46 (1992), pp. 167–174.
  • G. Celeux and J. Diebolt, A stochastic approximation type EM algorithm for the mixture problem, Stoch. Int. J. Probab. Stoch. Process. 41 (1992), pp. 119–134.
  • P. Dellaportas, J.J. Forster, and I. Ntzoufras, On Bayesian model and variable selection using MCMC, Stat. Comput. 12 (2002), pp. 27–36.
  • R. Dias, N.L. Garcia, G. Ludwig, and M.A. Saraiva, Aggregated functional data model for near-infrared spectroscopy calibration and prediction, J. Appl. Stat. 42 (2015), pp. 127–143.
  • R. Dias, N.L. Garcia, and A. Martarelli, Non-parametric estimation for aggregated functional data for electric load monitoring, Environmetrics 20 (2009), pp. 111–130.
  • F. Ferraty, Recent Advances in Functional Data Analysis and Related Topics, Physica Verlang, New York, 2011.
  • G. Franco, C.P. de Souza, and N.L. Garcia, Aggregated functional data model applied on clustering and disaggregation of UK electrical load profiles, preprint (2021). Available at arXiv, 2106.11448
  • K. Frončková and P. Pražák, Functional Data Analysis in Econometrics Vol. 11, University of Hradec Králové, 2021.
  • E. Fu and N. Heckman, Model-based curve registration via stochastic approximation EM algorithm, Comput. Stat. Data Anal. 131 (2019), pp. 159–175.
  • A. Gelman and D.B. Rubin, Inference from iterative simulation using multiple sequences, Stat. Sci. 7 (1992), pp. 457–511.
  • E.I. George and R.E. McCulloch, Variable selection via Gibbs sampling, J. Am. Stat. Assoc. 88 (1993), pp. 881–889.
  • E.I. George, R.E. McCulloch, and R.S. Tsay, Two approaches to Bayesian model selection with applications, Bayes. Anal. Stat. Econom. Essays Honor Arnold Zellner 309 (1996), pp. 339.
  • R. Ghosal, V.R. Varma, D. Volfson, I. Hillel, J. Urbanek, J.M. Hausdorff, A. Watts, and V. Zipunnikov, Distributional data analysis via quantile functions and its application to modelling digital biomarkers of gait in Alzheimer's Disease, preprint (2021). Availbale at arXiv, 2102.10783
  • G.H. Golub, M. Heath, and G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics 21 (1979), pp. 215–223.
  • T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer-Verlag, New York, NY, 2009.
  • A.E. Hoerl, Optimum solution of many variables equations, Chem. Eng. Prog. 55 (1959), pp. 69–78.
  • P.D. Hoff, A First Course in Bayesian Statistical Methods, Springer, New York, NY, 2009.
  • L. Horváth and P. Kokoszka, Inference for Functional Data with Applications, Springer, New York, NY, 2012.
  • H. Ishwaran and J.S. Rao, Detecting differentially expressed genes in microarrays using Bayesian model selection, J. Am. Stat. Assoc. 98 (2003), pp. 438–455.
  • H. Ishwaran and J.S. Rao, Spike and slab gene selection for multigroup microarray data, J. Am. Stat. Assoc. 100 (2005), pp. 764–780.
  • H. Ishwaran and J.S. Rao, Spike and slab variable selection: Frequentist and Bayesian strategies, Ann. Stat. 33 (2005), pp. 730–773.
  • A. Kucukelbir, D. Tran, R. Ranganath, A. Gelman, and D.M. Blei, Automatic differentiation variational inference, J. Mach. Learn. Res. 18 (2017), pp. 430–474.
  • L. Kuo and B. Mallick, Variable selection for regression models, Sankhyā Indian J. Stat. Ser. B 60 (1998), pp. 65–81.
  • M. Kyung, J. Gill, M. Ghosh, and G. Casella, Penalized regression, standard errors, and Bayesian Lassos, Bayes. Anal. 5 (2010), pp. 369–412.
  • A. Lenzi, C.P. de Souza, R. Dias, N.L. Garcia, and N.E. Heckman, Analysis of aggregated functional data from mixed populations with application to energy consumption, Environmetrics 28 (2016), pp. 1–14.
  • K. Li and S. Luo, Functional joint model for longitudinal and time-to-event data: An application to Alzheimer's disease, Stat. Med. 36 (2017), pp. 3560–3572.
  • N. Locantore, J. Marron, D. Simpson, N. Tripoli, J. Zhang, and K. Cohen, Robust principal component analysis for functional data, Test 8 (1999), pp. 1–73.
  • G. Malsiner-Walli and H. Wagner, Comparing spike and slab priors for Bayesian variable selection, Aust. J. Stat. 40 (2011), pp. 241–264.
  • M. Matabuena, A. Petersen, J.C. Vidal, and F. Gude, Glucodensities: A new representation of glucose profiles using distributional data analysis, Stat. Methods Med. Res. 30 (2021), pp. 1445–1464.
  • D. Nychka, Bayesian confidence intervals for smoothing splines, J. Am. Stat. Assoc. 83 (1988), pp. 1134–1143.
  • G. Obozinski, L. Jacob, and J.-P. Vert, Group Lasso with Overlaps: The Latent Group Lasso approach, Research report, inria-00628498, 2011.
  • R. O'Hara and M.J. Sillanpää, A review of Bayesian variable selection methods: What, how and which, Bayes. Anal. 4 (2009), pp. 85–118.
  • T. Park and G. Casella, The Bayesian Lasso, J. Am. Stat. Assoc. 103 (2008), pp. 681–686.
  • P.J. Green and B. Silverman, Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, London, 1994.
  • J. Ramsay, G. Hooker, and S. Graves, Functional Data Analysis with R and MATLAB, Springer Science and Business Media, New York, NY, 2009.
  • J. Ramsay and B. Silverman, Applied Functional Data Analysis: Methods and Case Studies, Springer, New York, NY, 2002.
  • J. Ramsay and B. Silverman, Functional Data Analysis, Springer, New York, 2005.
  • J.O. Ramsay and C.J. Dalzell, Some tools for functional data analysis, J. R. Stat. Soc. 53 (1991), pp. 539–572.
  • S. Robbiano, M. Saumard, and M. Curé, Improving prediction performance of stellar parameters using functional models, J. Appl. Stat. 43 (2016), pp. 1465–1476.
  • H. Shi, D. Ma, M. Faisal Beg, and J. Cao, A functional proportional hazard cure rate model for interval-censored data, Stat. Methods Med. Res. 31 (2022), pp. 154–168.
  • E. Sidrow, N. Heckman, S.M. Fortune, A.W. Trites, I. Murphy, and M. Auger-Méthé, Modelling multi‐scale, state‐switching functional data with hidden Markov models, Can. J. Stat. 50 (2022), pp. 327–356.
  • N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, A sparse-group lasso, J. Comput. Graph. Stat. 22 (2013), pp. 231–245.
  • C.P.E.D. Souza, N.E. Heckman, and F. XU, Switching nonparametric regression models for multi-curve data, Can. J. Stat. 45 (2017), pp. 442–460.
  • R. Talská, K. Hron, and T.M. Grygar, Compositional scalar-on-function regression with application to sediment particle size distributions, Math. Geosci. 53 (2021), pp. 1667–1695.
  • R. Talská, A. Menafoglio, J. Machalová, K. Hron, and E. Fišerová, Compositional regression with functional response, Comput. Stat. Data Anal. 123 (2018), pp. 66–85.
  • R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. 58 (1996), pp. 267–288.
  • G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, PA, 1990.
  • Y. Wang, J. Hu, K.-A. Do, and B.P. Hobbs, An efficient nonparametric estimate for spatially correlated functional data, Stat. Biosci. 11 (2019), pp. 162–183.
  • M. Yuan and Y. Lin, Model selection and estimation in regression with grouped variables, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 68 (2006), pp. 49–67.
  • H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67 (2005), pp. 301–320.
  • A Zygmund, Trigonometric Series, no. 1 in Cambridge Mathematical Library, Cambridge University Press, New York, NY, 2002.

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.