Correcting the Laplace Method with Variational Bayes

Niekerk, Janet van; Rue, Haåvard

doi:10.48550/arxiv.2111.12945

Cited by 3 publications

(5 citation statements)

References 28 publications

(40 reference statements)

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“…To evaluate the mesh, we used the production of triangles that appeared regular in size and shape (Krainski et al, 2019). To avoid computational errors, increase the stability of the program, and reduce computational time when running the models, we corrected the Laplace method with variational Bayes by setting inla.mode = "experimental" (Gaedke- Merzhäuser et al, 2022;Van Niekerk et al, 2022;Van Niekerk & Rue, 2021).…”

Section: Discussionmentioning

confidence: 99%

Spatial modeling of two mosquito vectors of West Nile virus using integrated nested Laplace approximations

et al. 2023

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The abundance of Culex restuans and Culex pipiens in relation to ecological predictors is poorly understood in regions of the United States where their ranges overlap. It is suspected that these species play different roles in spreading West Nile virus (WNV) in these regions, but few studies have modeled these species separately or accounted for spatial correlation using Bayesian methods. We used mosquito surveillance data collected by the Pennsylvania Department of Environmental Protection from 2002 to 2016 and integrated nested Laplace approximations with the stochastic partial differential equation approach to predict C. restuans and C. pipiens abundance in relation to several ecological predictors. We then made a predictive risk surface of abundance for each species at locations that were not sampled. Explanatory variables in the models included ecological variables previously described to be important predictors of the abundance of these mosquito species. Developed habitat, temperature, and precipitation were important predictor variables for the abundance of C. restuans, whereas developed habitat, snow water equivalent, and normalized difference water index were important predictor variables for the abundance of C. pipiens. The abundance of C. restuans had a negative relationship with developed habitat in contrast to C. pipiens abundance, which had a positive relationship with developed habitat. Julian date was modeled as a temporal trend for both species and showed C. restuans to be more abundant from late April through late June and C. pipiens to be more abundant from July through September. A seasonal crossover was observed between these two species on Julian day 185, 4 July. We observed different spatial patterns of abundance in the predictive risk maps of each of the species. Our results indicate that modeling the abundance of these species spatially and separately in regions where these two mosquito vectors coexist can help gain further insight into understanding the epidemiology of WNV in human and susceptible animal populations.

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Section: Discussionmentioning

confidence: 99%

Spatial modeling of two mosquito vectors of West Nile virus using integrated nested Laplace approximations

et al. 2023

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“…Additionally, it is possible to improve this approximation at every θ k using variational inference. Here, the mean of each p G (x|θ k , y) is updated by adding a correction term that is determined through solving a variational problem [50]. The posterior marginal distributions p(x j |y) are finally computed using information from each evaluation point {θ k } K k=1 and the respectively chosen approximations of p(x j |θ, y).…”

Section: Fundamentals Of the Inla Methodologymentioning

confidence: 99%

Parallelized integrated nested Laplace approximations for fast Bayesian inference

Gaedke-Merzhäuser

Niekerk²,

Schenk³

et al. 2022

Stat Comput

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There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of integrated nested Laplace approximations (INLA), a popular framework for performing approximate Bayesian inference on the class of Latent Gaussian models. Our approach makes use of nested thread-level parallelism, a parallel line search procedure using robust regression in INLA's optimization phase and the state-of-the-art sparse linear solver PARDISO. We leverage mutually independent function evaluations in the algorithm as well as advanced sparse linear algebra techniques. This way we can flexibly utilize the power of today's multi-core architectures. We demonstrate the performance of our new parallelization scheme on a number of different real-world applications. The introduction of parallelism leads to speedups of a factor 10 and more for all larger models. Our work is already integrated in the current version of the open-source R-INLA package, making its improved performance conveniently available to all users.

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“…The popularity of INLA lies in the fact that it allows fast approximate inference for LGMs. Furthermore, the INLA software is experiencing a new era, facilitated by the integration of novel techniques from Bayesian variational inference [25,26] and enhanced computation optimization, leading to improved parallel performance [27]. This section is devoted to briefly introducing the structure of LGMs and how INLA makes inference and prediction with the new advances in INLA.…”

Section: Lgms and Inlamentioning

confidence: 99%

“…Finally, the recent proposed Variational Bayes correction to Gaussian means by van Niekerk and Rue [25] is used to efficiently calculate an improved mean for the marginal posterior of the latent field. All this methodology can be used through R with the R-INLA package.…”

Section: Inlamentioning

confidence: 99%

“…Moreover, the integrated nested Laplace approximation (INLA) methodology [24], which is mainly intended for approximating the posterior distribution using the Laplace integration method, has become an alternative to MCMC guaranteeing a higher computational speed for Latent Gaussian Models (LGMs). With the incorporation of new techniques from Bayesian variational inference [25,26] and the optimisation of the computation, which improves its parallel performance [27], a new era is emerging in the INLA software. Hence, incorporating a tool for dealing with CoDa would be a convenient way to tackle the large CoDa databases sometimes encountered.…”

Section: Introductionmentioning

confidence: 99%

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A flexible Bayesian tool for CoDa mixed models: logistic-normal distribution with Dirichlet covariance

Martínez-Minaya,

Rue

2023

Preprint

Self Cite

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Compositional Data Analysis (CoDa) has gained popularity in recent years. This type of data consists of values from disjoint categories that sum up to a constant. Both Dirichlet regression and logistic-normal regression have become popular as CoDa analysis methods. However, fitting this kind of multivariate models presents challenges, especially when structured random effects are included in the model, such as temporal or spatial effects. To overcome these challenges, we propose the logistic-normal Dirichlet Model (LNDM). We seamlessly incorporate this approach into the R-INLA package, facilitating model fitting and model prediction within the framework of Latent Gaussian Models (LGMs). Moreover, we explore metrics like Deviance Information Criteria (DIC), Watanabe Akaike information criterion (WAIC), and cross-validation measure conditional predictive ordinate (CPO) for model selection in R-INLA for CoDa. Illustrating LNDM through a simple simulated example and with an ecological case study on Arabidopsis thaliana in the Iberian Peninsula, we underscore its potential as an effective tool for managing CoDa and large CoDa databases.

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Correcting the Laplace Method with Variational Bayes

Cited by 3 publications

References 28 publications

Spatial modeling of two mosquito vectors of West Nile virus using integrated nested Laplace approximations

Spatial modeling of two mosquito vectors of West Nile virus using integrated nested Laplace approximations

Parallelized integrated nested Laplace approximations for fast Bayesian inference

A flexible Bayesian tool for CoDa mixed models: logistic-normal distribution with Dirichlet covariance

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