Bayesian P-Splines

By Stefan Lang, Andreas Brezger. 2004

994 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/96b69a304c8f367d8cfcac229d1a61938066d1ab

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Citations in the corpus

Twenty years of P-splines (2015, methodology): “Bayesian P-splines were proposed by Lang and Brezger (2004), and they were made accessible by appropriate software (Brezger et al., 2005).”
Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models (2008, background): “…β, and Z, associated with b. Tensor product P-spline functions for higher-dimensional smooths (for example, bivariate interaction surfaces, spatial or spatio-temporal covariates) with a single smoothing parameter can be constructed and reparameterized in a similar fashion (Lang and Brezger, 2004).”
Bayesian semi parametric multi-state models (2008, background): “Lang & Brezger (2004) present a modified prior, where an additional weight is introduced for the variance of the error terms of the random walk priors (2.3) and (2.4).”
Correcting for spatial heterogeneity in plant breeding experiments with P-splines (2018, methodology): “In particular, the connection between SpATS and the first-differencing model in rows and columns proposed by Besag and Higdon (1999) becomes evident under the Bayesian formulation of P-splines (Lang and Brezger, 2004; Kneib, 2006).”
A Mixed Model Approach for Geoadditive Hazard Regression (2007, methodology): “A third alternative approach is based on two-dimensional tensor product P-splines, a rather parsimonious, but flexible method for modelling interactions between continuous covariates described in Lang & Brezger (2004) for Gaussian regression.”
Splines, knots, and penalties (2010, background): “Marx and Eilers (2002) found, in the context of multivariate calibration by penalized signal regression, markedly improved crossvalidation behavior.”
Bayesian structured additive distributional regression with an application to regional income inequality in Germany (2015, neutral): “,D with Gaussian errors εd ∼ N(0, τ 2) and noninformative priors for β1 or β1 and β2 [Lang and Brezger (2004)].”
Structured Additive Regression for Categorical Space–Time Data: A Mixed Model Approach (2006, methodology): “Lin and Zhang (1999) and Zhang (2004) used smoothing splines and random effects to model longitudinal data with responses from a univariate exponential family, Kammann and Wand (2003) introduced geoadditive models for Gaussian responses based on Gaussian random fields (GRFs) and P-splines, and Fahrm”
Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models (2011, methodology): “…smoothing parameters or variance parameters is moderate to large, then the simulation-based Bayesian approach of Fahrmeir, Lang and co-workers (e.g. Lang and Brezger (2004), Brezger and Lang (2006) and Fahrmeir and Lang (2001)) is likely to be more efﬁcient than the method that is proposed here,…”
Generalized structured additive regression based on Bayesian P-splines (2006, methodology): “The approach extends previous work by Lang and Brezger (2003) for Gaussian responses.”
BayesX: Analyzing Bayesian Structural Additive Regression Models (2005, methodology): “The functions f1 and f2 are the main effects of the two covariates and f1|2 is a two-dimensional interaction surface which can be modeled e.g. by twodimensional P-splines (Lang and Brezger 2004; Brezger and Lang 2005).”