Bayesian inference for generalized additive mixed models based on Markov random field priors

By Ludwig Fahrmeir, Stefan Lang. 2001

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Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Additive models with trend filtering (2017, methodology): “, Gu and Wahba [1991], Wood [2000], Fahrmeir and Lang [2001], Ruppert et al. [2003], Wood [2004], Kim and Gu [2004], Rue et al. [2009], Wood [2011], Wood et al. [2015, 2016]. Many of these papers use an efficient computational approach based on restricted maximum likelihood (REML) for selecting λj ,”
Possible decline in leatherback turtle Dermochelys coriacea nesting along the coast of Caribbean Central America (2004, methodology): “A nonparametric regression model using BayesX with Markov field random smoothness priors and a Bayesian smoothing spline was employed to calculate trends with 95% credible intervals (Fahrmeir & Lang, 2001; Balazs & Chaloupka, 2004).”
Generalized structured additive regression based on Bayesian P-splines (2006, methodology): “This paper can be seen as the final in a series of articles on Bayesian semiparametric regression based on smoothness priors and MCMC simulation techniques, see particularly Fahrmeir and Lang (2001a), Fahrmeir and Lang (2001b) and Lang and Brezger (2004). A very general class of models with structur”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, methodology): “, 2013), regression models with random effects (Fahrmeir and Lang, 2001), time-series models (West and Harrison, 1997), and selection between competing models based on Bayes factors (e.”
General design Bayesian generalized linear mixed models (2006, background): “Those known to us are Zeger and Karim (1991), Clayton (1996), Diggle, Tawn and Moyeed (1998) and Fahrmeir and Lang (2001).”
Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape (2013, methodology): “Bayesian inference is based on highly efficient Markov chain simulation based on iteratively weighted least squares proposals as suggested by Gamerman (1997) or Brezger and Lang (2006) and for the models at hand in a recent paper by Klein et al.”
Smoothing Parameter and Model Selection for General Smooth Models (2015, methodology): “But Greven and Kneib (2010) showed that this is overly likely to select complex models, especially when the model contains random effects: the difficulty arises because τ0 neglects the fact that the smoothing parameters have been estimated and are, therefore, uncertain (a marginal AIC based on the f”
PENALIZED STRUCTURED ADDITIVE REGRESSION FOR SPACE-TIME DATA: A BAYESIAN PERSPECTIVE (2004, methodology): “Fahrmeir and Lang (2001b)) is given by ηit = f1(xit1) + · · ·+ fk(xitk) + ftime(t) + fspat(sit) + uitγ (4) where ftime is a possibly nonlinear time trend and fspat is a spatially correlated (random) effect of the location sit an observation pertains to. Models with a predictor that contains a spatia”
Bayesian semi parametric multi-state models (2008, methodology): “For updating the parameter vectors corresponding to time-independent functions f (h) k , as well as fixed effects γ (h) and frailty terms b, we use a slightly modified version of the Metropolis–Hastings algorithm based on iteratively weighted least squares (IWLS) proposals, developed for fixed and r”
Somatic growth dynamics of West Atlantic hawksbill sea turtles: a spatio‐temporal perspective (2016, background): “…enables arbitrary specification of the functional form for each continuous covariate included in the model, and accounts for mixed effects from multiple measurements on the same sampling unit such as location (Fahrmeir and Lang 2001) and each individual turtle (Chaloupka and Balazs 2005).”
Inference in Semiparametric Dynamic Models for Binary Longitudinal Data (2006, methodology): “Third, Markov process priors are conceptually simple and adaptable to different orders, so as to meet problem-specific tasks (Besag et al. 1995; Fahrmeir and Lang 2001).”
Coverage Properties of Confidence Intervals for Generalized Additive Model Components (2012, methodology): “As an alternative, Fahrmeir et al. (2004) and Fahrmeir & Lang (2001) adopted the fully Bayesian approach, which employs MCMC for practical computations.”
Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data (2014, methodology): “We can then use the following Fisher scoring algorithm (Fahrmeir and Lang 2001) to find the Gaussian approximation.”
Modeling Spatiotemporal Forest Health Monitoring Data (2009, methodology): “Because the GAMM can be expressed as a generalized linear mixed model (GLMM) [as in eq.”