The Generalized Jackknife: Finite Samples and Subsample Sizes

Sharot, Trevor

doi:10.1080/01621459.1976.10480367

Cited by 16 publications

(6 citation statements)

References 7 publications

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“…To estimate the null hypothesis distribution, a N × N matrix λ n,j was first estimated for each of the C subjects of the control database. The null distribution for each network n and CRSN j was then estimated using a generalized jackknife approach (Sharot, 1976 ). To do so, 2/3rd of the control sample was randomly selected to calculate the mean and standard deviation and one target sample was randomly selected among the remaining 1/3rd to compute the metric λ n,j under the null hypothesis.…”

Section: Methodsmentioning

confidence: 99%

Detection of abnormal resting-state networks in individual patients suffering from focal epilepsy: an initial step toward individual connectivity assessment

et al. 2014

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The spatial coherence of spontaneous slow fluctuations in the blood-oxygen-level dependent (BOLD) signal at rest is routinely used to characterize the underlying resting-state networks (RSNs). Studies have demonstrated that these patterns are organized in space and highly reproducible from subject to subject. Moreover, RSNs reorganizations have been suggested in pathological conditions. Comparisons of RSNs organization have been performed between groups of subjects but have rarely been applied at the individual level, a step required for clinical application. Defining the notion of modularity as the organization of brain activity in stable networks, we propose Detection of Abnormal Networks in Individuals (DANI) to identify modularity changes at the individual level. The stability of each RSN was estimated using a spatial clustering method: Bootstrap Analysis of Stable Clusters (BASC) (Bellec et al., 2010). Our contributions consisted in (i) providing functional maps of the most stable cores of each networks and (ii) in detecting “abnormal” individual changes in networks organization when compared to a population of healthy controls. DANI was first evaluated using realistic simulated data, showing that focussing on a conservative core size (50% most stable regions) improved the sensitivity to detect modularity changes. DANI was then applied to resting state fMRI data of six patients with focal epilepsy who underwent multimodal assessment using simultaneous EEG/fMRI acquisition followed by surgery. Only patient with a seizure free outcome were selected and the resected area was identified using a post-operative MRI. DANI automatically detected abnormal changes in 5 out of 6 patients, with excellent sensitivity, showing for each of them at least one “abnormal” lateralized network closely related to the epileptic focus. For each patient, we also detected some distant networks as abnormal, suggesting some remote reorganization in the epileptic brain.

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Section: Methodsmentioning

confidence: 99%

Detection of abnormal resting-state networks in individual patients suffering from focal epilepsy: an initial step toward individual connectivity assessment

et al. 2014

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“…They focused on the bias, precision and accuracy of the seven jackknife estimators (Brose et al, 2003). Magnussen et al (2006) evaluated the generalized jackknife estimator, which is a linear combination of conventional jackknife estimators (Sharot, 1976). Chao (1987) found that the jackknife estimators were severely negatively biased for small sample sizes but performed better with increasing sample size.…”

Section: Jackknife Species Richness Estimatorsmentioning

confidence: 99%

“…The general procedure is re-estimating a parameter using only subsets of the samples, combining the new and the original estimates suitably weighted and producing a final estimate which is more accurate (Sharot, 1976). The method was originally developed by Quenouille (1956) and was later coined as ''jackknife'' by Tukey (1958).…”

Section: Jackknife Species Richness Estimatorsmentioning

confidence: 99%

Estimation of tree species richness from large area forest inventory data: Evaluation and comparison of jackknife estimators

Lam

Kleinn

2008

Forest Ecology and Management

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“…Where U K−j is (K − j)-samples bound averaged over all possible choices of a subset of size K − j from ψ 1:K , and c(K, J, j) are Sharot coefficients (Sharot, 1976;Nowozin, 2018): Proof. First, we note that U K can be represented as marginal log-density plus some non-negative (due to theorem A.1) bias, which we'll consider in greater detail.…”

Section: E Debiasing the Bound E1 Deriving The Boundmentioning

confidence: 99%

Importance Weighted Hierarchical Variational Inference

Sobolev,

Vetrov

2019

Preprint

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Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior distribution. In turn, the expressivity of the variational family is largely limited by the requirement of having a tractable density function. To overcome this roadblock, we introduce a new family of variational upper bounds on a marginal log density in the case of hierarchical models (also known as latent variable models). We then give an upper bound on the Kullback-Leibler divergence and derive a family of increasingly tighter variational lower bounds on the otherwise intractable standard evidence lower bound for hierarchical variational distributions, enabling the use of more expressive approximate posteriors. We show that previously known methods, such as Hierarchical Variational Models, Semi-Implicit Variational Inference and Doubly Semi-Implicit Variational Inference can be seen as special cases of the proposed approach, and empirically demonstrate superior performance of the proposed method in a set of experiments.

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The Generalized Jackknife: Finite Samples and Subsample Sizes

Cited by 16 publications

References 7 publications

Detection of abnormal resting-state networks in individual patients suffering from focal epilepsy: an initial step toward individual connectivity assessment

Detection of abnormal resting-state networks in individual patients suffering from focal epilepsy: an initial step toward individual connectivity assessment

Estimation of tree species richness from large area forest inventory data: Evaluation and comparison of jackknife estimators

Importance Weighted Hierarchical Variational Inference

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