The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
Bayesian P-Splines
Abstract
P-splines are an attractive approach for modeling nonlinear smooth effects of covariates within the additive and varying coefficient models framework. In this article, we first develop a Bayesian version for P-splines and generalize in a second step the approach in various ways. First, the assumption of constant smoothing parameters can be replaced by allowing the smoothing parameters to be locally adaptive. This is particularly useful in situations with changing curvature of the underlying smooth function or with highly oscillating functions. In a second extension, one-dimensional P-splines are generalized to two-dimensional surface fitting for modeling interactions between metrical covariates. In a last step, the approach is extended to situations with spatially correlated responses allowing the estimation of geoadditive models. Inference is fully Bayesian and uses recent MCMC techniques for drawing random samples from the posterior. In a couple of simulation studies the performance of Bayesian P-splines is studied and compared to other approaches in the literature. We illustrate the approach by two complex application on rents for flats in Munich and on human brain mapping.
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Cites
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Multivariate Adaptive Regression Splines
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Bayesian image restoration, with two applications in spatial statistics
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Flexible smoothing with B-splines and penalties
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Bayesian Analysis of Binary and Polychotomous Response Data
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On Gibbs sampling for state space models
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Cited by
Rue, H., Martino, S., & Chopin, N. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00700.x · Cited by 5,279
Morris, J. S. (2015) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-010814-020413 · Cited by 423
Generalized structured additive regression based on Bayesian P-splines
Brezger, A., & Lang, S. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2004.10.011 · Cited by 371
Self-citationShape constrained additive models
Pya, N., & Wood, S. N. (2015) · Statistics and Computing · doi:10.1007/s11222-013-9448-7 · Cited by 315
Correcting for spatial heterogeneity in plant breeding experiments with P-splines
Rodríguez-Álvarez, M. X., Boer, M. P., van Eeuwijk, F. A., & Eilers, P. H. C. (2018) · Spatial Statistics · doi:10.1016/j.spasta.2017.10.003 · Cited by 309
Metadata
- Authors
- Lang, S., & Brezger, A.
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 2004-03
- Volume
- 13
- Issue
- 1
- Pages
- 183-212
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W2119047368
- Cited by
- 865
- References
- 38
- FWCI
- 26.57
- Type
- journal article
- Language
- en
- Open access
- closed
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