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Laplace Approximation (laplace + approximation)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2009
Håvard Rue
Summary., Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. [source]

A Version of the EM Algorithm for Proportional Hazard Model with Random Effects

BIOMETRICAL JOURNAL, Issue 6 2005
José Cortiñas Abrahantes
Abstract Proportional hazard models with multivariate random effects (frailties) acting multiplicatively on the baseline hazard have recently become a topic of an intensive research. One of the main practical problems related to the models is the estimation of parameters. To this aim, several approaches based on the EM algorithm have been proposed. The major difference between these approaches is the method of the computation of conditional expectations required at the E-step. In this paper an alternative implementation of the EM algorithm is proposed, in which the expected values are computed with the use of the Laplace approximation. The method is computationally less demanding than the approaches developed previously. Its performance is assessed based on a simulation study and compared to a non-EM based estimation approach proposed by Ripatti and Palmgren (2000). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Joint Inference on HIV Viral Dynamics and Immune Suppression in Presence of Measurement Errors

BIOMETRICS, Issue 2 2010
L. Wu
Summary:, In an attempt to provide a tool to assess antiretroviral therapy and to monitor disease progression, this article studies association of human immunodeficiency virus (HIV) viral suppression and immune restoration. The data from a recent acquired immune deficiency syndrome (AIDS) study are used for illustration. We jointly model HIV viral dynamics and time to decrease in CD4/CD8 ratio in the presence of CD4 process with measurement errors, and estimate the model parameters simultaneously via a method based on a Laplace approximation and the commonly used Monte Carlo EM algorithm. The approaches and many of the points presented apply generally. [source]

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2009
Håvard Rue
Summary., Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. [source]