@article{Wood2015Smoothing,
 abstract = {This paper discusses a general framework for smoothing parameter estimation

for models with regular likelihoods constructed in terms of unknown smooth

functions of covariates. Gaussian random effects and parametric terms may also

be present. By construction the method is numerically stable and convergent,

and enables smoothing parameter uncertainty to be quantified. The latter

enables us to fix a well known problem with AIC for such models. The smooth

functions are represented by reduced rank spline like smoothers, with

associated quadratic penalties measuring function smoothness. Model estimation

is by penalized likelihood maximization, where the smoothing parameters

controlling the extent of penalization are estimated by Laplace approximate

marginal likelihood. The methods cover, for example, generalized additive

models for non-exponential family responses (for example beta, ordered

categorical, scaled t distribution, negative binomial and Tweedie

distributions), generalized additive models for location scale and shape (for

example two stage zero inflation models, and Gaussian location-scale models),

Cox proportional hazards models and multivariate additive models. The framework

reduces the implementation of new model classes to the coding of some standard

derivatives of the log likelihood.},
 author = {Wood, Simon N. and Pya, Natalya and S{\"a}fken, Benjamin},
 year = {2016},
 title = {Smoothing Parameter and Model Selection for General Smooth Models},
 url = {http://dx.doi.org/10.1080/01621459.2016.1180986},
 keywords = {phd;stat},
 pages = {1548--1563},
 volume = {111},
 number = {516},
 issn = {0162-1459},
 journal = {Journal of the American Statistical Association},
 doi = {10.1080/01621459.2016.1180986},
 howpublished = {refereed}
}

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The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for non-exponential family responses (for example beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (for example two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. 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Gaussian random effects and parametric terms may also\r\n\r\nbe present. By construction the method is numerically stable and convergent,\r\n\r\nand enables smoothing parameter uncertainty to be quantified. The latter\r\n\r\nenables us to fix a well known problem with AIC for such models. The smooth\r\n\r\nfunctions are represented by reduced rank spline like smoothers, with\r\n\r\nassociated quadratic penalties measuring function smoothness. Model estimation\r\n\r\nis by penalized likelihood maximization, where the smoothing parameters\r\n\r\ncontrolling the extent of penalization are estimated by Laplace approximate\r\n\r\nmarginal likelihood. The methods cover, for example, generalized additive\r\n\r\nmodels for non-exponential family responses (for example beta, ordered\r\n\r\ncategorical, scaled t distribution, negative binomial and Tweedie\r\n\r\ndistributions), generalized additive models for location scale and shape (for\r\n\r\nexample two stage zero inflation models, and Gaussian location-scale models),\r\n\r\nCox proportional hazards models and multivariate additive models. The framework\r\n\r\nreduces the implementation of new model classes to the coding of some standard\r\n\r\nderivatives of the log likelihood.},\r\n author = {Wood, Simon N. and Pya, Natalya and S{\\\"a}fken, Benjamin},\r\n year = {2016},\r\n title = {Smoothing Parameter and Model Selection for General Smooth Models},\r\n url = {http://dx.doi.org/10.1080/01621459.2016.1180986},\r\n keywords = {phd;stat},\r\n pages = {1548--1563},\r\n volume = {111},\r\n number = {516},\r\n issn = {0162-1459},\r\n journal = {Journal of the American Statistical Association},\r\n doi = {10.1080/01621459.2016.1180986},\r\n howpublished = {refereed}\r\n}\r\n\r\n\r\n","author_short":["Wood, S. 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