Bayesian inference for generalized linear mixed models

Fong, Youyi; Rue, Håvard; Wakefield, Jon

doi:10.1093/biostatistics/kxp053

Cited by 225 publications

(208 citation statements)

References 26 publications

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“…Fong et al, 2010). In our stationary versus non-stationary setting, we can use the simulation study to investigate the quality of the rule of thumb that the difference should be at least ten in favour of the more complex model for this to be chosen.…”

Section: Simulation Studymentioning

confidence: 99%

Spatial models with explanatory variables in the dependence structure

2014

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Please cite this article as: Ingebrigtsen, R., Lindgren, F., Steinsland, I., Spatial models with explanatory variables in the dependence structure. Spatial Statistics (2013), http://dx.doi.org/10. 1016/j.spasta.2013.06.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractGeostatistical models have traditionally been stationary. However, physical knowledge about underlying spatial processes often require models with nonstationary dependence structures. Thus, there has been an interest in the literature to provide flexible models and computationally efficient methods for non-stationary phenomena. In this work, we demonstrate that the stochastic partial differential equation (SPDE) approach to spatial modelling provides a flexible class of non-stationary models where explanatory variables easily can be included in the dependence structure. In addition, the SPDE approach enables computationally efficient Bayesian inference with integrated nested Laplace approximations (INLA) available through the R-package r-inla. We illustrate the suggested modelling framework with a case study of annual precipitation in southern Norway, and compare a non-stationary model with dependence structure governed by elevation to a stationary model. Further, we use a simulation study to explore the annual precipitation models. We investigate identifiability of model parameters and whether the deviance information criterion (DIC) is able to distinguish datasets from the non-stationary and stationary models.

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Section: Simulation Studymentioning

confidence: 99%

Spatial models with explanatory variables in the dependence structure

2014

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“…A practical limitation to data analysis using MCMC, especially for complex data sets, is the large computational burden. Fong et al [35] propose integrated nested Laplace approximation, which combines Laplace approximations and numerical integration, as a computationally efficient alternative to MCMC methods. They conclude that their approximation strategy is accurate in general, but may be less accurate for binomial data with small denominators.…”

Section: Accounting For Overdispersionmentioning

confidence: 99%

Overdispersion

Dean

Lundy

2016

Wiley StatsRef: Statistics Reference Online

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Count data analyzed under a Poisson assumption or data in the form of proportions analyzed under a binomial assumption often exhibit overdispersion, where the empirical variance in the data is greater than that predicted by the model. This entry illustrates how overdispersion may arise and discusses the consequences of ignoring it, in particular, the underestimation of standard errors of covariate effects. Straightforward methods for ascertaining whether overdispersion is evident are presented. Simple methods for incorporating overdispersion within the framework of quasi‐likelihood estimation are reviewed as well as generalized linear mixed models, which form a broad scheme for model‐based analysis when overdispersion is present.

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“…Standard approaches rely on numerical integration [65] or Laplace approximation [66,67], but neither strategy scales well with the increasing dimension of the integral, which in our case is equal to the sample size. Because of this problem, standard implementations of binomial mixed models often produce biased estimates and overly narrow (i.e., anti-conservative) confidence intervals [68][69][70][71][72]. To overcome this problem, we instead use a Markov chain Monte Carlo (MCMC) algorithm-based approach for inference, using un-informative priors for the hyper-parameters h 2 and σ 2 .…”

Section: The Binomial Mixed Model and The Macau Algorithmmentioning

confidence: 99%

A flexible, efficient binomial mixed model for identifying differential DNA methylation in bisulfite sequencing data

Lea

Alberts

Tung

et al. 2015

Preprint

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Identifying sources of variation in DNA methylation levels is important for understanding gene regulation. Recently, bisulfite sequencing has become a popular tool for investigating DNA methylation levels. However, modeling bisulfite sequencing data is complicated by dramatic variation in coverage across sites and individual samples, and because of the computational challenges of controlling for genetic covariance in count data. To address these challenges, we present a binomial mixed model and an efficient, sampling-based algorithm (MACAU: Mixed model association for count data via data augmentation) for approximate parameter estimation and p-value computation. This framework allows us to simultaneously account for both the over-dispersed, count-based nature of bisulfite sequencing data, as well as genetic relatedness among individuals. Using simulations and two real data sets (whole genome bisulfite sequencing (WGBS) data from Arabidopsis thaliana and reduced representation bisulfite sequencing (RRBS) data from baboons), we show that our method provides well-calibrated test statistics in the presence of population structure. Further, it improves power to detect differentially methylated sites: in the RRBS data set, MACAU detected 1.6-fold more age-associated CpG sites than a beta-binomial model (the next best approach). Changes in these sites are consistent with known age-related shifts in DNA methylation levels, and are enriched near genes that are differentially expressed with age in the same population. Taken together, our results indicate that MACAU is an efficient, effective tool for analyzing bisulfite sequencing data, with particular salience to analyses of structured populations. MACAU is freely available at www.xzlab. org/software.html. Author SummaryDNA methylation is an important epigenetic modification involved in regulating gene expression. It can be measured at base-pair resolution, on a genome-wide scale, by coupling sodium bisulfite conversion with high-throughput sequencing (a technique known as 'bisulfite sequencing'). However, the data generated by such methods present several challenges for statistical analysis. In particular, while the raw data generated from bisulfite sequencing experiments are read counts, they are often converted to proportions for ease of modeling, resulting in loss of information. Furthermore, although DNA methylation levels are known to be heritable-and are thus affected by kinship and population structure-existing approaches for modeling bisulfite sequencing data fail to account for this covariance. Such failure can lead to spurious associations and reduced power. Here, we present a new approach that models bisulfite sequencing data using raw read counts, while also taking into account population structure and other sources of data over-dispersion. Using simulations and two real data sets (publicly available data from Arabidopsis thaliana and newly generated data from Papio cynocephalus), we demonstrate that our model provides well-calibrated p-values and i...

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Bayesian inference for generalized linear mixed models

Cited by 225 publications

References 26 publications

Spatial models with explanatory variables in the dependence structure

Spatial models with explanatory variables in the dependence structure

Overdispersion

A flexible, efficient binomial mixed model for identifying differential DNA methylation in bisulfite sequencing data

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