A Powerful Bayesian Test for Equality of Means in High Dimensions

Zoh, Roger S.; Sarkar, Abhra; Carroll, Raymond J.; Mallick, Bani K.

doi:10.1080/01621459.2017.1371024

Cited by 18 publications

(20 citation statements)

References 24 publications

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“…And a regression model with a smaller MAE was better than that with a large MAE. Considering the "large p small n" paradigm in the Omic studies [35][36][37], the principle of parsimony (Ocam's razor) preferred a simpler model [38]. So a prediction model was better than that with a similar performance metrics and a larger number of features.…”

Section: B Performance Evaluation Metricsmentioning

confidence: 99%

Survival Time Prediction of Breast Cancer Patients Using Feature Selection Algorithm Crystall

Liu

Zheng

et al. 2021

IEEE Access

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Breast cancer is one of main causes of death for women. Most of the existing survival analyses focus on the features' associations with whether the patients may survive five years or not. The personalized question remains largely unresolved about how long a breast cancer patient will live. This study aims to predict the patient-specific survival time of breast cancer patients. It formulates the personalized question into two machine learning problems. The first problem is the binary classification of whether a patient will live longer than five years or not. The second one is to build a regression model to predict the patient's survival time within five years. The methylome of a breast cancer patient is used for the prediction. A new algorithm Crystall is presented to find the methylomic features for this regression model. Our models perform well in the above two problems, and achieve the mean absolute error (MAE) of about 1 month for predicting how long a breast cancer patient will live within five years. The detected biomarker genes demonstrate close connections with breast cancers.

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Section: B Performance Evaluation Metricsmentioning

confidence: 99%

Survival Time Prediction of Breast Cancer Patients Using Feature Selection Algorithm Crystall

Liu

Zheng

et al. 2021

IEEE Access

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“…Zoh et al . () discuss tests for high‐dimensional data. In contrast, the size of the

t

‐test of the focused hypothesis

H_{0 F} : {bold-italicγ}^{T} Δ = 0

based on PC scores can be close to the naive level or grossly distorted.…”

Section: Critical Assessment and Conclusionmentioning

confidence: 99%

“…One conclusion is that the size of the t-test holds under the global hypothesis: H Δ 0 : = but that the test has poor power. Hotelling's T 2 is a better choice in low-dimensional settings Zoh et al (2018). discuss tests for high-dimensional data.…”

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confidence: 99%

Data reduction prior to inference: Are there consequences of comparing groups using a t‐test based on principal component scores?

Bedrick

2019

Biometrics

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Researchers often use a two‐step process to analyze multivariate data. First, dimensionality is reduced using a technique such as principal component analysis, followed by a group comparison using a t‐test or analysis of variance. Although this practice is often discouraged, the statistical properties of this procedure are not well understood, starting with the hypothesis being tested. We suggest that this approach might be considering two distinct hypotheses, one of which is a global test of no differences in the mean vectors, and the other being a focused test of a specific linear combination where the coefficients have been estimated from the data. We study the asymptotic properties of the two‐sample t‐statistic for these two scenarios, assuming a nonsparse setting. We show that the size of the global test agrees with the presumed level but that the test has poor power. In contrast, the size of the focused test can be arbitrarily distorted with certain mean and covariance structures. A simple method is provided to correct the size of the focused test. Data analyses and simulations are used to illustrate the results. Recommendations on the use of this two‐step method and the related use of principal components for prediction are provided.

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“…This approach works by projecting the originally high dimensional data to a low-dimensional embedding and perform the test in this lower dimension data, completely eliminating the need to inverse a rank degenerate sample covariance matrix. Reference of paper using this approach in the two group testing setting are Lopes et al (2011); Thulin (2014); Srivastava et al (2016) in the frequentist setting and Zoh et al (2018) in the Bayesian setting. Recently, there is a growing effort towards combining these two approach in the two-group mean testing problem (Hu et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…See Wan et al, 2020;López-Sánchez et al, 2021 to list just a few. Additionally, RP have already been proven very successful in the two-sample group tests Lopes et al (2011);Srivastava et al (2016); Zoh et al (2018). However, to the best of our knowledge, they have not been used or evaluated in the multiple (MANOVA) groups mean testing problem.…”

Section: Introductionmentioning

confidence: 99%

An approximate Bayes factor based high dimensional MANOVA using Random Projections

Zoh¹

2022

Preprint

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High-dimensional mean vector testing problem for two or more groups remain a very active research area. In these setting, traditional tests are not applicable because they involve the inversion of rank deficient group covariance matrix. In current approaches, this problem is addressed by simply looking at a test assuming a sparse or diagonal covariance matrix potentially ignoring complex dependency between features. In this paper, we develop a Bayes factor (BF) based testing procedure for comparing two or more population means in (very) high dimensional settings. Two versions of the Bayes factor based test statistics are considered which are based on a Random projection (RP) approach. RPs are appealing since they make not assumption about the form of the dependency across features in the data. The final test statistic is based on an ensemble of Bayes factors corresponding to multiple replications of randomly projected data. Both proposed test statistics are compared through a battery of simulation settings. Finally they are applied to the analysis of a publicly available genomic single cell RNA-seq (scRNA-seq) dataset.

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A Powerful Bayesian Test for Equality of Means in High Dimensions

Cited by 18 publications

References 24 publications

Survival Time Prediction of Breast Cancer Patients Using Feature Selection Algorithm Crystall

Survival Time Prediction of Breast Cancer Patients Using Feature Selection Algorithm Crystall

Data reduction prior to inference: Are there consequences of comparing groups using a t‐test based on principal component scores?

An approximate Bayes factor based high dimensional MANOVA using Random Projections

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