Sampling from the posterior distribution in generalized linear mixed models

By Dani Gamerman. 1997

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Citations in the corpus

A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use (2010, methodology): “For models with random slopes, a Metropolis– Hastings with iteratively weighted least square proposal densities has been shown to efficiently sample vectors of random effects (Gamerman, 1997).”
PENALIZED STRUCTURED ADDITIVE REGRESSION FOR SPACE-TIME DATA: A BAYESIAN PERSPECTIVE (2004, methodology): “For updating the parameters in an MCMC sampler, we use an MH-algorithm based on iteratively weighted least squares (IWLS) proposals introduced by Gamerman (1997) and adapted to the present situation in Brezger and Lang (2003).”
Bayesian varying-coefficient models using adaptive regression splines (2001, methodology): “…or deleting a tj;lþ1 with changing kj by 1 and corresponding changes in cj; the choice between birth and death is done randomly. iii) Update of basis coefficients: update the basis coefficients cj by the method of Gamerman (1997a) for GLM’s adapted to blocks of fixed effects (without change in kj).”
Bayesian Structured Additive Distributional Regression (2013, methodology): “To construct suitable proposal densities, we follow the idea of iteratively weighted least squares proposals [Gamerman, 1997, Brezger and Lang, 2006] and construct local quadratic approximations to the full conditionals.”
Beyond mean regression (2013, background): “…weighted least squares proposals based on a quadratic approximation of the full conditional are generally a good alternative that automatically adapts to the form of the full conditional without requiring the manual tuning of proposal hyperparameters (Gamerman, 1997; Brezger and Lang, 2006).”
Monotonic Regression Based on Bayesian P–Splines (2008, methodology): “An IWLS proposal is obtained by a quadratic approximation of the likelihood via Taylor expansion around the current state βcj of βj , compare Brezger and Lang (2003) or, in the mixed model context, Gamerman (1997).”
Bayesian auxiliary variable models for binary and multinomial regression (2006, methodology): “Alternative strategies for the logistic model include Gamerman (1997) who uses a normal approximation to the posterior density of the regression coecien ts found using iterative-reweighted-least-squares and Dellaportas and Smith (1993) who suggest the use of adaptive-rejection sampling (ARS) from ”
Geoadditive Survival Models (2006, methodology): “…βspat, fixed effects γ , and random effects b, we use a slightly modified version of an MH algorithm based on iteratively weighted least squares (IWLS) proposals, developed for fixed and random effects by Gamerman (1997) and adapted to generalized additive mixed models by Brezger and Lang (2006).”
Bayesian semi parametric multi-state models (2008, methodology): “…a slightly modified version of the Metropolis–Hastings algorithm based on iteratively weighted least squares (IWLS) proposals, developed for fixed and random effects in generalised linear mixed models by Gamerman (1997) and adapted to generalised additive mixed models in Brezger and Lang (2006).”
Bayesian inference for generalized additive mixed models based on Markov random field priors (2001, background): “An alternative is the weighted least squaresproposal suggested by Gamerman (1997).”
Modern Applied Statistics with S Fourth edition (2002, methodology): “Independent component analysis Independent component analysis (ICA) was named by Comon (1994), and has since become a ‘hot’ topic in data visualization; see the books Lee (1998); Hyvärinenet al. (2001) and the expositions by Hyv ̈ arinen and Oja (2000) and Hastieet al.”
Journal of the American Statistical Association Bayesian Inference for Logistic Models Using Pólya–gamma Latent Variables Bayesian Inference for Logistic Models Using P ´ Olya–gamma Latent Variables (unknown): “Of course, it is certainly possible to design and tune better MH samplers for mixed models; see, for example, Gamerman (1997).”
Bayesian analysis of measurement error models using integrated nested Laplace approximations (2015, methodology): “Here, samples for the regression coefficients β = .β0, βx, βz/ were obtained on the basis of the block sampling algorithm by Gamerman (1997).”