Bayesian Methods for High Dimensional Linear Models

Mallick, Himel; Yi, Nengjun

doi:10.4172/2155-6180.s1-005

Cited by 20 publications

(12 citation statements)

References 107 publications

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“…This is the graphical LASSO prior of [ 13 ]: where is an indicator function that O is positive definite, Exp( x | λ ) has the exponential density of the form p ( x ) = λe − λx 1 x >0 , and Laplace ( x | λ ) has the Laplace density of the form . In comparison to variable selection priors such as spike-and-slab [ 18 ], the graphical LASSO prior is more scalable to high dimensions at the cost of being unable to generate estimates that are exactly zero [ 19 ]. We deal with this by using the resulting posterior samples to conclude whether a correlation is likely to be zero or not.…”

Section: Banocc: Bayesian Analysis Of Compositional Covariancementioning

confidence: 99%

A Bayesian method for detecting pairwise associations in compositional data

2017

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Compositional data consist of vectors of proportions normalized to a constant sum from a basis of unobserved counts. The sum constraint makes inference on correlations between unconstrained features challenging due to the information loss from normalization. However, such correlations are of long-standing interest in fields including ecology. We propose a novel Bayesian framework (BAnOCC: Bayesian Analysis of Compositional Covariance) to estimate a sparse precision matrix through a LASSO prior. The resulting posterior, generated by MCMC sampling, allows uncertainty quantification of any function of the precision matrix, including the correlation matrix. We also use a first-order Taylor expansion to approximate the transformation from the unobserved counts to the composition in order to investigate what characteristics of the unobserved counts can make the correlations more or less difficult to infer. On simulated datasets, we show that BAnOCC infers the true network as well as previous methods while offering the advantage of posterior inference. Larger and more realistic simulated datasets further showed that BAnOCC performs well as measured by type I and type II error rates. Finally, we apply BAnOCC to a microbial ecology dataset from the Human Microbiome Project, which in addition to reproducing established ecological results revealed unique, competition-based roles for Proteobacteria in multiple distinct habitats.

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Section: Banocc: Bayesian Analysis Of Compositional Covariancementioning

confidence: 99%

A Bayesian method for detecting pairwise associations in compositional data

2017

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“…We will standardize predictors and then set a weakly informative prior for all coefficients: a Normal distribution centred on zero, with a standard deviation of 2. This corresponds with the prior belief that any given coefficient is likely to be small, while allowing for a coefficient to be larger if the data support it; it is broadly equivalent to (weakly regularizing) ridge regression in the frequentist framework (Mallick & Yi, 2013). For all standard deviations of group-level random effects, we will use the corresponding default priors, which are "used (a) to be only very weakly informative in order to influence results as few as possible, while (b) providing at least some regularization to considerably improve convergence and sampling efficiency"…”

Section: Analytic Approach: Bayesian Logistic Mixed Effects Regressionmentioning

confidence: 99%

Does the motor system functionally contribute to keeping words in working memory? A pre-registered replication of Shebani and Pulvermüller (2013, Cortex)

Montero-Melis¹,

Paridon²,

Ostarek³

et al. 2019

Preprint

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Increasing evidence implicates the sensorimotor systems with high-level cognition, but the extent to which these systems play a functional role remains debated. Using an elegant design, Shebani and Pulvermüller (2013) reported that carrying out a demanding rhythmic task with the hands led to selective impairment of working memory for hand-related words (e.g., clap), while carrying out the same task with the feet led to selective memory impairment for foot-related words (e.g., kick). This striking double dissociation constitutes strong evidence for an embodied account of working memory, a system that has received scarce attention in the embodiment literature. However, the original study was likely underpowered and used suboptimal statistical analyses, raising questions about the robustness of the results. In fact, our Bayesian reanalysis with a more appropriate model yields inconclusive evidence for the effect (BF10 = 1.7). To re-examine this seminal finding, we here attempt an appropriately powered, fully pre-registered replication of the original study, following a sequential design with a maximal participant sample size over seven times that of the original (108 vs. 15). We will analyse the results with Bayesian generalized mixed models and use Bayes factors to quantify the evidence in support of the effect predicted by theories of embodied cognition.

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“…which correspond to (7) the value of the longitudinal outcome, (8) the slope, and (9) the area parameterization. Both the value and the slope are included in (10). The baseline risk was simulated from a Weibull distribution h 0 (t) = t −1 with = 1.65.…”

Section: Designmentioning

confidence: 99%

“…Despite their popularity in applied research, it has long been recognized that these algorithms have several drawbacks [8]. Hence, research in the last few years has focused on alternative approaches and predominantly on so-called regularization methods [9,10]. From the frequentist point of view, these methods can be seen as techniques to improve the least-squares estimator by adding constraints to the value of the coefficients to reduce the variance of the resulting estimates.…”

Section: Introductionmentioning

confidence: 99%

Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures

Andrinopoulou

Rizopoulos

2016

Statist. Med.

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The joint modeling of longitudinal and survival data has recently received much attention. Several extensions of the standard joint model that consists of one longitudinal and one survival outcome have been proposed including the use of different association structures between the longitudinal and the survival outcomes. However, in general, relatively little attention has been given to the selection of the most appropriate functional form to link the two outcomes. In common practice, it is assumed that the underlying value of the longitudinal outcome is associated with the survival outcome. However, it could be that different characteristics of the patients' longitudinal profiles influence the hazard. For example, not only the current value but also the slope or the area under the curve of the longitudinal outcome. The choice of which functional form to use is an important decision that needs to be investigated because it could influence the results. In this paper, we use a Bayesian shrinkage approach in order to determine the most appropriate functional forms. We propose a joint model that includes different association structures of different biomarkers and assume informative priors for the regression coefficients that correspond to the terms of the longitudinal process. Specifically, we assume Bayesian lasso, Bayesian ridge, Bayesian elastic net, and horseshoe. These methods are applied to a dataset consisting of patients with a chronic liver disease, where it is important to investigate which characteristics of the biomarkers have an influence on survival. Copyright © 2016 John Wiley & Sons, Ltd.

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Bayesian Methods for High Dimensional Linear Models

Cited by 20 publications

References 107 publications

A Bayesian method for detecting pairwise associations in compositional data

A Bayesian method for detecting pairwise associations in compositional data

Does the motor system functionally contribute to keeping words in working memory? A pre-registered replication of Shebani and Pulvermüller (2013, Cortex)

Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures

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