IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v019i02.html
   My bibliography  Save this article

Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package

Author

Listed:
  • Paciorek, Christopher J.

Abstract

The spectral representation of stationary Gaussian processes via the Fourier basis provides a computationally efficient specification of spatial surfaces and nonparametric regression functions for use in various statistical models. I describe the representation in detail and introduce the spectralGP package in R for computations. Because of the large number of basis coefficients, some form of shrinkage is necessary; I focus on a natural Bayesian approach via a particular parameterized prior structure that approximates stationary Gaussian processes on a regular grid. I review several models from the literature for data that do not lie on a grid, suggest a simple model modification, and provide example code demonstrating MCMC sampling using the spectralGP package. I describe reasons that mixing can be slow in certain situations and provide some suggestions for MCMC techniques to improve mixing, also with example code, and some general recommendations grounded in experience.

Suggested Citation

  • Paciorek, Christopher J., 2007. "Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i02).
  • Handle: RePEc:jss:jstsof:v:019:i02
    DOI: http://hdl.handle.net/10.18637/jss.v019.i02
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v019i02/v19i02.pdf
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v019i02/spectralGP_1.1.tar.gz
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v019i02/Code.zip
    Download Restriction: no

    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v019.i02?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Victor De Oliveira & Zifei Han, 2023. "Approximate reference priors for Gaussian random fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 296-326, March.
    2. Silas Bergen & Lianne Sheppard & Joel D. Kaufman & Adam A. Szpiro, 2016. "Multipollutant measurement error in air pollution epidemiology studies arising from predicting exposures with penalized regression splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 731-753, November.
    3. Sigrist, Fabio & Künsch, Hans R. & Stahel, Werner A., 2015. "spate: An R Package for Spatio-Temporal Modeling with a Stochastic Advection-Diffusion Process," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i14).
    4. Thomas Kneib & Nadja Klein & Stefan Lang & Nikolaus Umlauf, 2019. "Modular regression - a Lego system for building structured additive distributional regression models with tensor product interactions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 1-39, March.
    5. Anyosa, Susan & Eidsvik, Jo & Pizarro, Oscar, 2023. "Adaptive spatial designs minimizing the integrated Bernoulli variance in spatial logistic regression models - with an application to benthic habitat mapping," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    6. repec:jss:jstsof:36:i13 is not listed on IDEAS
    7. Maitreyee Bose & James S. Hodges & Sudipto Banerjee, 2018. "Toward a diagnostic toolkit for linear models with Gaussian‐process distributed random effects," Biometrics, The International Biometric Society, vol. 74(3), pages 863-873, September.

    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:jss:jstsof:v:019:i02. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.