Two-Component Mixture Model in the Presence of Covariates

Deb, Nabarun; Saha, Sujayam; Guntuboyina, Adityanand; Sen, Bodhisattva

doi:10.1080/01621459.2021.1888739

Cited by 8 publications

(6 citation statements)

References 45 publications

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“…We develop the asymptotics using the following Bayesian model (Deb et al., 2018; Ferkingstad et al., 2008; Lei & Fithian, 2018), which we call the conditional two‐groups model and which extends the two‐groups model of Storey (2003) and Efron et al. (2001):

\begin{matrix} X_{i} \sim {double-struckP}^{X}, H_{i} | false(X_{i} = x false) \sim Bernoulli false(1 ‐ π_{0} (x) false), \\ P_{i} false| (H_{i} = 0, X_{i} = x) \sim U [0, 1], P_{i} false| false(H_{i} = 1, X_{i} = x false) \sim F_{normalalt} false(\cdot false| X_{i} = x false) \end{matrix}

We also define

F false(t false| X_{i} = x false) = π_{0} false(x false) t + false(1 ‐ π_{0} (x) false) F_{normalalt} false(t false| X_{i} = x false)

: the distribution of

P_{i}

given

X_{i} = x

.…”

Section: Weighted and Cross‐weighted Multiple Testingmentioning

confidence: 99%

Covariate Powered Cross-Weighted Multiple Testing

Ignatiadis

Huber

2021

Journal of the Royal Statistical Society Series B: Statistical Methodology

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\begin{matrix} X_{i} \sim {double-struckP}^{X}, H_{i} | false(X_{i} = x false) \sim Bernoulli false(1 ‐ π_{0} (x) false), \\ P_{i} false| (H_{i} = 0, X_{i} = x) \sim U [0, 1], P_{i} false| false(H_{i} = 1, X_{i} = x false) \sim F_{normalalt} false(\cdot false| X_{i} = x false) \end{matrix}

We also define

F false(t false| X_{i} = x false) = π_{0} false(x false) t + false(1 ‐ π_{0} (x) false) F_{normalalt} false(t false| X_{i} = x false)

: the distribution of

P_{i}

given

X_{i} = x

.…”

Section: Weighted and Cross‐weighted Multiple Testingmentioning

confidence: 99%

Covariate Powered Cross-Weighted Multiple Testing

Ignatiadis

Huber

2021

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…However, the first estimation step poses significant challenges as it boils down to a hard density regression problem (Dunson et al, 2007). For example, to estimate

{f}_x\left(\cdotp \right)

(or equivalently

{h}_x\left(\cdotp \right)

), a line of works (Deb et al, 2021; Scott et al, 2015; Tansey et al, 2018) proceeds by assuming a fixed alternative density, i.e.

{f}_{1,x}(z)\equiv {f}_1(z),

to make way for the application of an EM algorithm.…”

Section: Data‐driven Zap Proceduresmentioning

confidence: 99%

ZAP:Z-Value Adaptive Procedures for False Discovery Rate Control with Side Information

Leung

Sun

2022

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Adaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognised that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with p‐values as their main statistics. However, for two‐sided hypotheses, the usual data processing step that transforms the primary statistics, known as z‐values, into p‐values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a z‐value based covariate‐adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the z‐values and covariates. It seeks to emulate the oracle z‐value procedure via a working model, and its rejection regions significantly depart from those of the p‐value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state‐of‐the‐art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with p‐value‐based methods. Our methodology is implemented in the R package zap.

show abstract

“…However, the first estimation step poses significant challenges as it boils down to a hard density regression problem (Dunson et al, 2007). For example, to estimate f x p¨q (or equivalently h x p¨q), a line of works (Deb et al, 2021, Scott et al, 2015, Tansey et al, 2018 proceeds by assuming a fixed alternative density, i.e.…”

Section: Data-driven Zap Proceduresmentioning

confidence: 99%

ZAP: $Z$-value Adaptive Procedures for False Discovery Rate Control with Side Information

Leung¹,

Sun²

2021

Preprint

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Adaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognized that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with p-values as their main statistics. However, for two-sided hypotheses, the usual data processing step that transforms the primary statistics, known as z-values, into p-values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a z-value based covariate-adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the z-values and covariates. It seeks to emulate the oracle z-value procedure via a working model, and its rejection regions significantly depart from those of the p-value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state-of-the-art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with p-value based methods. Our methodology is implemented in the R package zap.

show abstract

Two-Component Mixture Model in the Presence of Covariates

Cited by 8 publications

References 45 publications

Covariate Powered Cross-Weighted Multiple Testing

Covariate Powered Cross-Weighted Multiple Testing

ZAP:Z-Value Adaptive Procedures for False Discovery Rate Control with Side Information

ZAP: $Z$-value Adaptive Procedures for False Discovery Rate Control with Side Information

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