IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i12p5100-5120.html
   My bibliography  Save this article

A flexible approach to Bayesian multiple curve fitting

Author

Listed:
  • Botts, Carsten H.
  • Daniels, Michael J.

Abstract

We model sparse functional data from multiple subjects with a mixed-effects regression spline. In this model, the expected values for any subject (conditioned on the random effects) can be written as the sum of a population curve and a subject-specific deviate from this population curve. The population curve and the subject-specific deviates are both modeled as free-knot b-splines with k and k' knots located at and , respectively. To identify the number and location of the "free" knots, we sample from the posterior using reversible jump MCMC methods. Sampling from this posterior distribution is complicated, however, by the flexibility we allow for the model's covariance structure. No restrictions (other than positive definiteness) are placed on the covariance parameters [psi] and [sigma]2 and, as a result, no analytical form for the likelihood exists. In this paper, we consider two approximations to and then sample from the corresponding approximations to . We also sample from which has a likelihood that is available in closed form. While sampling from this larger posterior is less efficient, the resulting marginal distribution of knots is exact and allows us to evaluate the accuracy of each approximation. We then consider a real data set and explore the difference between and the more accurate approximation to .

Suggested Citation

  • Botts, Carsten H. & Daniels, Michael J., 2008. "A flexible approach to Bayesian multiple curve fitting," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5100-5120, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5100-5120
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00257-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jamie L. Bigelow & David B. Dunson, 2007. "Bayesian Adaptive Regression Splines for Hierarchical Data," Biometrics, The International Biometric Society, vol. 63(3), pages 724-732, September.
    2. Crainiceanu, Ciprian M. & Ruppert, David & Wand, Matthew P., 2005. "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i14).
    3. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    4. D. G. T. Denison & B. K. Mallick & A. F. M. Smith, 1998. "Automatic Bayesian curve fitting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 333-350.
    5. Dominici F. & Daniels M. & Zeger S. L. & Samet J. M., 2002. "Air Pollution and Mortality: Estimating Regional and National Dose-Response Relationships," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 100-111, March.
    6. John A. Rice & Colin O. Wu, 2001. "Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, The International Biometric Society, vol. 57(1), pages 253-259, March.
    7. Sam Behseta & Robert E. Kass & Garrick L. Wallstrom, 2005. "Hierarchical models for assessing variability among functions," Biometrika, Biometrika Trust, vol. 92(2), pages 419-434, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dhiman Bhadra & Michael J. Daniels & Sungduk Kim & Malay Ghosh & Bhramar Mukherjee, 2012. "A Bayesian Semiparametric Approach for Incorporating Longitudinal Information on Exposure History for Inference in Case–Control Studies," Biometrics, The International Biometric Society, vol. 68(2), pages 361-370, June.
    2. Bellio, Ruggero & Grassetti, Luca, 2011. "Semiparametric stochastic frontier models for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 71-83, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bruno Scarpa & David B. Dunson, 2014. "Enriched Stick-Breaking Processes for Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 647-660, June.
    2. Basna, Rani & Nassar, Hiba & Podgórski, Krzysztof, 2022. "Data driven orthogonal basis selection for functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Janet Niekerk & Haakon Bakka & Håvard Rue, 2023. "Stable Non-Linear Generalized Bayesian Joint Models for Survival-Longitudinal Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 102-128, February.
    4. Johnson, Matthew S., 2007. "Modeling dichotomous item responses with free-knot splines," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4178-4192, May.
    5. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
    6. Anestis Antoniadis & Irène Gijbels & Mila Nikolova, 2011. "Penalized likelihood regression for generalized linear models with non-quadratic penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 585-615, June.
    7. Amato, Umberto & Antoniadis, Anestis & De Feis, Italia & Goude, Yannig & Lagache, Audrey, 2021. "Forecasting high resolution electricity demand data with additive models including smooth and jagged components," International Journal of Forecasting, Elsevier, vol. 37(1), pages 171-185.
    8. Alexandre Rodrigues & Peter Diggle & Renato Assuncao, 2010. "Semiparametric approach to point source modelling in epidemiology and criminology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 533-542, May.
    9. Erin E. Gabriel & Michael J. Daniels & M. Elizabeth Halloran, 2016. "Comparing biomarkers as trial level general surrogates," Biometrics, The International Biometric Society, vol. 72(4), pages 1046-1054, December.
    10. Sarah Brown & Pulak Ghosh & Bhuvanesh Pareek & Karl Taylor, 2017. "Financial Hardship and Saving Behaviour: Bayesian Analysis of British Panel Data," Working Papers 2017011, The University of Sheffield, Department of Economics.
    11. Jaroslaw Harezlak & Louise M. Ryan & Jay N. Giedd & Nicholas Lange, 2005. "Individual and Population Penalized Regression Splines for Accelerated Longitudinal Designs," Biometrics, The International Biometric Society, vol. 61(4), pages 1037-1048, December.
    12. Ye, Mao & Lu, Zhao-Hua & Li, Yimei & Song, Xinyuan, 2019. "Finite mixture of varying coefficient model: Estimation and component selection," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 452-474.
    13. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    14. Svajone Bekesiene & Ieva Meidute-Kavaliauskiene, 2022. "Artificial Neural Networks for Modelling and Predicting Urban Air Pollutants: Case of Lithuania," Sustainability, MDPI, vol. 14(4), pages 1-24, February.
    15. Wei Liu & Lang Wu, 2007. "Simultaneous Inference for Semiparametric Nonlinear Mixed-Effects Models with Covariate Measurement Errors and Missing Responses," Biometrics, The International Biometric Society, vol. 63(2), pages 342-350, June.
    16. Roger Peng & Leah Welty & Aidan McDermott, 2004. "The National Morbidity, Mortality, and Air Pollution Study Database in R," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1044, Berkeley Electronic Press.
    17. Esra Kürüm & Danh V. Nguyen & Qi Qian & Sudipto Banerjee & Connie M. Rhee & Damla Şentürk, 2024. "Spatiotemporal multilevel joint modeling of longitudinal and survival outcomes in end-stage kidney disease," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 827-852, October.
    18. Pena, Daniel & Redondas, Dolores, 2006. "Bayesian curve estimation by model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 688-709, February.
    19. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
    20. Lindstrom, Mary J., 2002. "Bayesian estimation of free-knot splines using reversible jumps," Computational Statistics & Data Analysis, Elsevier, vol. 41(2), pages 255-269, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5100-5120. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.