Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

Abstract

Alzheimer's disease can be diagnosed by analyzing brain images (eg, magnetic resonance imaging, MRI) and neuropsychological tests (eg, mini‐mental state examination, MMSE). A partially linear mean shift model (PLMSM) is here proposed to investigate the relationship between MMSE score and high‐dimensional regions of interest in MRI, and detect the outliers. In the presence of high‐dimensional data, existing Bayesian approaches (eg, Markov chain Monte Carlo) to analyze a PLMSM take intensive computational cost and require huge memory, and have low convergence rate. To address these issues, a variational Bayesian inference is developed to simultaneously estimate parameters and nonparametric functions and identify outliers in a PLMSM. A Bayesian P‐splines method is presented to approximate nonparametric functions, a Bayesian adaptive Lasso approach is employed to select predictors, and outliers are detected by the classification variable. Two simulation studies are conducted to assess the finite sample performance of the proposed method. An MRI dataset with elderly cognitive ability is provided to corroborate the proposed method.

Semiparametric normal transformation joint model of multivariate longitudinal and bivariate time‐to‐event data

“…It is suggest to take the hyperparameter a m 𝜍 = 1 and a relatively small value for the hyperparameter b m 𝜍 (eg, b m 𝜍 = 0.001, 0.005, or 0.00001) leading to an almost diffuse prior for 𝜍 2 m . 25,30 To identify the important covariates associated with joint model, we here specify the Laplace priors 22 for the components of…”

“…Here the prior for $$$ {\varsigma}_m^{-2} $$$ is assumed to follow a Gamma distribution, that is, $$$ {\varsigma}_m^{-2}\sim \Gamma \left({a}_{\varsigma}^m,{b}_{\varsigma}^m\right) $$$, where $$$ {a}_{\varsigma}^m $$$ and $$$ {b}_{\varsigma}^m $$$ are the prespecified hyperparameters for $$$ m=1,2 $$$. It is suggest to take the hyperparameter $$$ {a}_{\varsigma}^m=1 $$$ and a relatively small value for the hyperparameter $$$ {b}_{\varsigma}^m $$$ (eg, $$$ {b}_{\varsigma}^m=0.001,0.005 $$$, or 0.00001) leading to an almost diffuse prior for $$$ {\varsigma}_m^2 $$$ 25,30 …”

Variational inference on a Bayesian adaptive lasso Tobit quantile regression model

“…An especially popular variational family consists of distributions under which the model parameters are independent, the so‐called mean‐field variational Bayes. Recent reviews of VB include Blei et al (2017), Ostwald et al (2014), Tran et al (2021) and Fox and Roberts (2012), Wu and Tang (2021).…”

Variational Bayesian Inference in High-Dimensional Linear Mixed Models

“…Its basic idea is to transform the high-dimensional integration problem into an optimization problem in making Bayesian inference and then optimize the evidence lower bound (ELB), which is efficiently computed, and finally utilize the ELB to obtain a variational approximation to the posterior distribution in Bayesian analysis. The variational Bayesian approach has been applied to some familiar models, for example, latent variable models [24], mixtures of factor analysis [25], graphical models [26] and partially linear mean shift models with high-dimensional data [27].…”