Bayesian inferences for beta semiparametric‐mixed models to analyze longitudinal neuroimaging data

Wang, Xiao Feng; Li, Yingxing

doi:10.1002/bimj.201300003

Cited by 4 publications

(3 citation statements)

References 37 publications

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“…INLA approach has been applied to a variety of complex models, such as spatial-temporal disease mapping (Schrödle and Held, 2011), additive mixed quantile regression models (Yue and Rue, 2011), and beta semiparametric mixed models (Wang and Li, 2013). INLA, as new Bayesian computation tools, have a great potential to be used in many scientific fields.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Nonparametric Regression and Density Estimation Using Integrated Nested Laplace Approximations

Wang

2013

J Biomet Biostat

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Integrated nested Laplace approximations (INLA) are a recently proposed approximate Bayesian approach to fit structured additive regression models with latent Gaussian field. INLA method, as an alternative to Markov chain Monte Carlo techniques, provides accurate approximations to estimate posterior marginals and avoid time-consuming sampling. We show here that two classical nonparametric smoothing problems, nonparametric regression and density estimation, can be achieved using INLA. Simulated examples and R functions are demonstrated to illustrate the use of the methods. Some discussions on potential applications of INLA are made in the paper.

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Section: Discussionmentioning

confidence: 99%

Bayesian Nonparametric Regression and Density Estimation Using Integrated Nested Laplace Approximations

Wang

2013

J Biomet Biostat

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“…Many studies have investigated the influence of predictors on a vector of proportions, or percentages, or fractions [10,24,25]. It is often inappropriate to apply a Gaussian error model for situations when the response is restricted to the interval (0, 1).…”

Section: The Generalized Mixed-effects Varying Coefficient Modelmentioning

confidence: 99%

Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates

Wang

et al. 2013

Journal of Applied Statistics

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This paper is motivated from a neurophysiological study of muscle fatigue, in which biomedical researchers are interested in understanding the time-dependent relationships of handgrip force and electromyography measures. A varying coefficient model is appealing here to investigate the dynamic pattern in the longitudinal data. The response variable in the study is continuous but bounded on the standard unit interval (0, 1) over time, while the longitudinal covariates are contaminated with measurement errors. We propose a generalization of varying coefficient models for the longitudinal proportional data with errorsin-covariates. We describe two estimation methods with penalized splines, which are formalized under a Bayesian inferential perspective. The first method is an adaptation of the popular regression calibration approach. The second method is based on a joint likelihood under the hierarchical Bayesian model. A simulation study is conducted to evaluate the efficacy of the proposed methods under different scenarios. The analysis of the neurophysiological data is presented to demonstrate the use of the methods.

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“…Because it is bounded between 0 and 1, y ij (x) is assumed to follow a beta distribution, which is capable of flexibly modeling this type of data (Wang and Li, 2014). Being interested in the visit effect on FA profiles in the RCST region, we consider the following one-way functional ANOVA model: for x ∈ X ⊂ IR, where Beta(µ, λ) denotes the beta distribution with mean µ and variance…”

Section: Diffusion Tensor Imagingmentioning

confidence: 99%

Bayesian Generalized Two-way ANOVA Modeling for Functional Data Using INLA

Yu¹,

Bolin²,

Rue³

2019

STAT SINICA

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Functional analysis of variance (ANOVA) modeling has been proved particularly useful to investigate the dynamic changes of functional data according to certain categorical factors and their interactions. However, the current existing methods often encounter difficulties when the functional data are high-dimensional, non-Gaussian, and/or exhibit certain shape characteristics that vary with spatial locations. In this paper, we investigate the functional two-way ANOVA models from a novel Bayesian perspective. A class of highly flexible Gaussian Markov random fields (GMRF) are taken as priors on the functions in the model, which allows us to model various types of functional effects, such as (discrete or continuous) temporal effects and (point-level or areal) spatial effects. The resulting posterior distributions are obtained by an efficient computational tool based on integrated nested Laplace approximations (INLA) (Rue et al., 2009). We then employ the excursion method introduced by Bolin and Lindgren (2015) to build simultaneous credible intervals of functional effects and test their significance from a Bayesian point of view. A simulation study and multiple real data examples are presented to demonstrate the merits of our method.

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Bayesian inferences for beta semiparametric‐mixed models to analyze longitudinal neuroimaging data

Cited by 4 publications

References 37 publications

Bayesian Nonparametric Regression and Density Estimation Using Integrated Nested Laplace Approximations

Bayesian Nonparametric Regression and Density Estimation Using Integrated Nested Laplace Approximations

Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates

Bayesian Generalized Two-way ANOVA Modeling for Functional Data Using INLA

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