Approximate inference for disease mapping

Ainsworth, Laurie; Dean, C. B.

doi:10.1016/j.csda.2005.05.001

Cited by 23 publications

(16 citation statements)

References 14 publications

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“…This suggests that a cruder approximation based on a Gaussian approximation to π.θ|y/ is not sufficiently accurate for our purposes; this also applies to similar approximations that are based on 'equivalent Gaussian observations' around x Å , and evaluated at the mode of expression (3) (Breslow and Clayton, 1993;Ainsworth and Dean, 2006). A critical aspect of our approach is to explore and manipulateπ.θ|y/ andπ.x i |y/ in a 'non-parametric' way.…”

Section: Inference: the New Approachmentioning

confidence: 99%

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Rue

Martino

Chopin

2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

4,294

4,451

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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.

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Section: Inference: the New Approachmentioning

confidence: 99%

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Rue

Martino

Chopin

2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

4,294

4,451

View full text Add to dashboard Cite

show abstract

“…In disease mapping, inference about random parameters are of interest. Ainsworth and Dean (2006) showed that an advantage of using the PQL method over the Bayesian methods was in it's ability to give a reasonably accurate inference for small-area relative risks. Even though unreported we see in Table 7 that the h-likelihood method improves its coverage rate by using a better dispersion estimator.…”

Section: Scottish Lip Cancer Datamentioning

confidence: 98%

A comparison of the hierarchical likelihood and Bayesian approaches to spatial epidemiological modelling

et al. 2007

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SUMMARYRecently Bayesian methods have been widely used in disease mapping. Hierarchical (h-) likelihood methods allow reliable likelihood inference in random-effect models and it is therefore interesting to compare h-likelihood and Bayesian methods. For comparison we consider three examples: low birth weight and cancer mortality data in South Carolina and lip cancer data in Scotland. Mean estimates from both h-likelihood and Bayesian approaches are almost identical, while variance-component estimates can be somewhat different, depending upon choice of priors.

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“…One topic that has received much attention lately is inference and prediction for the spatial generalized linear mixed model (GLMM), see for instance Diggle et al (1998) and Christensen et al (2006) for a Bayesian view, Breslow & Clayton (1993) and Zhang (2002) for a frequentist analogy, and Ainsworth & Dean (2006) and Paciorek (2007) who compared penalized likelihood methods with Bayesian solutions using Markov chain Monte Carlo (MCMC) simulations. The common model can briefly be described as follows: let x represent a latent variable at n spatial sites on a two-dimensional domain.…”

Section: Introductionmentioning

confidence: 99%

Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models

Eidsvik

Martino

Rue

2009

Scandinavian J Statistics

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In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical special case with a high dimensional latent spatial variable and observations at only a few known registration sites. Our methods of inference are deterministic, using no random sampling.We present two methods of approximate inference. The first is very fast to compute and via examples we find that this approximation is 'practically sufficient'. By this expression we mean that the results obtained by this approximate method do not show any bias or dispersion effects that might affect decision making. The other approximation is an improved version of the first one, and via examples we demonstrate that the inferred posterior approximations of this improved version are 'practically exact'. By this expression we mean that one would have to run Markov chain Monte Carlo simulations for longer than is typically done to detect any indications of bias or dispersion error effects in the approximate results.The two methods of approximate inference can help to expand the scope of geostatistical models, for instance in the context of model choice, model assessment, and sampling design. The approximations take seconds of CPU time, in sharp contrast to overnight Markov chain Monte Carlo runs for solving these types of problems. Our approach to approximate inference could easily be part of standard softwares.

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Approximate inference for disease mapping

Cited by 23 publications

References 14 publications

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations

A comparison of the hierarchical likelihood and Bayesian approaches to spatial epidemiological modelling

Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models

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