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Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 79 (16 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper 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 nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo 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
Simultaneous credible bands for latent Gaussian models
, 2010
"... Deterministic Bayesian inference for latent Gaussian models has recently become available using integrated nested Laplace approximations (INLA). Applying the INLAmethodology, marginal estimates for elements of the latent field can be computed efficiently, providing relevant summary statistics like p ..."
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Cited by 2 (0 self)
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Deterministic Bayesian inference for latent Gaussian models has recently become available using integrated nested Laplace approximations (INLA). Applying the INLAmethodology, marginal estimates for elements of the latent field can be computed efficiently, providing relevant summary statistics like posterior means, variances and pointwise credible intervals. In this paper, we extend the use of INLA to joint inference and present an algorithm to derive analytical simultaneous credible bands for subsets of the latent field. The algorithm is based on approximating the joint distribution of the subsets by multivariate Gaussian mixtures. Additionally, we present a saddlepoint approximation to compute Bayesian contour probabilities, representing the posterior support of fixed parameter vectors of interest. The given methods are applied to various examples from the literature.
The function ‘hhh4 ’ in the Rpackage ‘surveillance’
, 2012
"... This document gives an introduction to the use of the function hhh4 for modelling univariate and multivariate time series of infectious disease counts. The function is part of the Rpackage surveillance, which provides tools for the visualization, modelling and monitoring of surveillance time series ..."
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This document gives an introduction to the use of the function hhh4 for modelling univariate and multivariate time series of infectious disease counts. The function is part of the Rpackage surveillance, which provides tools for the visualization, modelling and monitoring of surveillance time series. The basic functionality of surveillance is introduced in the package vignette (Höhle et al., 2007) and in Höhle (2007) with main focus on outbreak detection methods. The following illustrates the use of hhh4 as estimation and prediction routine for the modelling framework proposed by Held et al. (2005), and extended in Paul et al. (2008), Paul and Held (2011) and Herzog et al. (2011). 1
For personal use only.
"... Estimating species composition and quantifying uncertainty in multispecies fisheries: hierarchical Bayesian models for stratified sampling protocols with missing data ..."
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Estimating species composition and quantifying uncertainty in multispecies fisheries: hierarchical Bayesian models for stratified sampling protocols with missing data
Submitted to the Annals of Applied Statistics arXiv: math.PR/0000000 MODELING TEMPORAL GRADIENTS IN REGIONALLY AGGREGATED CALIFORNIA ASTHMA HOSPITALIZATION DATA
"... enormous recent burgeoning of spatialtemporal databases and associated statistical modeling. Here we depart from the rather rich literature in spacetime modeling by considering the setting where space is discrete (e.g. aggregated data over regions), but time is continuous. Our major objective in t ..."
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enormous recent burgeoning of spatialtemporal databases and associated statistical modeling. Here we depart from the rather rich literature in spacetime modeling by considering the setting where space is discrete (e.g. aggregated data over regions), but time is continuous. Our major objective in this application is to carry out inference on gradients of a temporal process in our dataset of monthly county level asthma hospitalization rates in the state of California, while at the same time accounting for spatial similarities of the temporal process across neighboring counties. Use of continuous time models here allows inference at a finer resolution than at which the data are sampled. Rather than use parametric forms to model time, we opt for a more flexible stochastic process embedded within a dynamic Markov random field framework. Through the matrixvalued covariance function we can ensure that the temporal process realizations are mean square differentiable, and may thus carry out inference on temporal gradients in a posterior predictive fashion. We use this approach to evaluate temporal gradients where we are concerned with temporal changes in the residual and fitted rate curves after accounting for seasonality, spatiotemporal ozone levels, and several spatiallyresolved important sociodemographic covariates.
Working Paper 11/11NonParametric Estimation of Forecast Distributions in NonGaussian, Nonlinear State Space Models
, 2011
"... The object of this paper is to produce nonparametric maximum likelihood estimates of forecast distributions in a general nonGaussian, nonlinear state space setting. The transition densities that de…ne the evolution of the dynamic state process are represented in parametric form, but the condition ..."
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The object of this paper is to produce nonparametric maximum likelihood estimates of forecast distributions in a general nonGaussian, nonlinear state space setting. The transition densities that de…ne the evolution of the dynamic state process are represented in parametric form, but the conditional distribution of the nonGaussian variable is estimated nonparametrically. The …ltering and prediction distributions are estimated via a computationally e ¢ cient algorithm that exploits the functional relationship between the observed variable, the state variable and a measurement error with an invariant distribution. Simulation experiments are used to document the accuracy of the nonparametric method relative to both correctly and incorrectly speci…ed parametric alternatives. In an empirical illustration, the method is used to produce sequential estimates of the forecast distribution of realized volatility on the S&P500 stock index during the recent …nancial crisis. A resampling technique for measuring sampling variation in the estimated forecast