An upper bound for the probability of a union

Hunter, David

doi:10.1017/s0021900200104164

Cited by 78 publications

(97 citation statements)

References 6 publications

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“…The P-value approximation, based on upcrossings (Rice 1945), improved Bonferroni inequalities (Hunter 1976;Worsley 1982;Efron 1997), Euler characteristics (Adler 1981), or the Weyl-Hotelling tube formula (Sun 1993;Sun and Loader 1994), is…”

Section: Z(s) a Zero Mean Unit Variance Gaussian Random Field And mentioning

confidence: 99%

Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping

Taylor

Worsley

2007

Journal of the American Statistical Association

128

136

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Brain mapping data have been modeled as Gaussian random fields, and local increases in mean are detected by local maxima of a random field of test statistics derived from this data. Accurate P-values for local maxima are readily available for isotropic data based on the expected Euler characteristic of the excursion set of the test statistic random field. In this paper we give a simple method for dealing with non-isotropic data. Our approach has connections to the Sampson and Guttorp (1992) model for non-isotropy in which there exists an unknown mapping of the support of the data to a space in which the random fields are isotropic. Heuristic justification for our approach comes from the Nash Embedding Theorem. Formally we show that our method gives consistent unbiased estimators for the true P-values based on new results of Taylor and Adler (2003) for random fields on manifolds which replace the Euclidean metric by the variogram. The results are used to detect gender differences in the cortical thickness of the brain, and to detect regions of the brain involved in sentence comprehension measured by fMRI.

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Section: Z(s) a Zero Mean Unit Variance Gaussian Random Field And mentioning

confidence: 99%

Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping

Taylor

Worsley

2007

Journal of the American Statistical Association

128

136

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“…This theorem was first proven for m = 2 by Hunter (1976) and later extended to m > 2 by Hoover (1987). The theorem is Theorem A-I.…”

Section: Approach I Intersection Subtractionmentioning

confidence: 86%

Different Algorithms for Obtaining Upper Bounds to Multivariate Normal Areas Outside of Origin Centered Rectangles Using Joint Marginal Probabilities

Hoover¹

1988

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“…After generating the reconstructions, a probability that each reconstruction is correct (termed the accuracy of the reconstruction) is predicted, using Hunter's bound (Hunter, 1976) (see the Supplementary section S4 for the definition of the accuracy of reconstructions). Hunter's bound can be calculated from relatively simple statistics that are readily learned from a small set of PSMs (about 5000 PSMs).…”

Section: Generating De Novo Reconstructionsmentioning

confidence: 99%

UniNovo : A Universal Tool for de Novo Peptide Sequencing

Jeong

Kim

Pevzner

2013

Lecture Notes in Computer Science

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Motivation: Mass spectrometry (MS) instruments and experimental protocols are rapidly advancing, but de novo peptide sequencing algorithms to analyze tandem mass (MS/MS) spectra are lagging behind. Although existing de novo sequencing tools perform well on certain types of spectra [e.g. Collision Induced Dissociation (CID) spectra of tryptic peptides], their performance often deteriorates on other types of spectra, such as Electron Transfer Dissociation (ETD), Higher-energy Collisional Dissociation (HCD) spectra or spectra of non-tryptic digests. Thus, rather than developing a new algorithm for each type of spectra, we develop a universal de novo sequencing algorithm called UniNovo that works well for all types of spectra or even for spectral pairs (e.g. CID/ETD spectral pairs). UniNovo uses an improved scoring function that captures the dependences between different ion types, where such dependencies are learned automatically using a modified offset frequency function. Results: The performance of UniNovo is compared with PepNovoþ, PEAKS and pNovo using various types of spectra. The results show that the performance of UniNovo is superior to other tools for ETD spectra and superior or comparable with others for CID and HCD spectra. UniNovo also estimates the probability that each reported reconstruction is correct, using simple statistics that are readily obtained from a small training dataset. We demonstrate that the estimation is accurate for all tested types of spectra (including CID, HCD, ETD, CID/ETD and HCD/ETD spectra of trypsin, LysC or AspN digested peptides). Availability: UniNovo is implemented in JAVA and tested on Windows, Ubuntu and OS X machines. UniNovo is available at http://proteomics. ucsd.edu/Software/UniNovo.html along with the manual.

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An upper bound for the probability of a union

Cited by 78 publications

References 6 publications

Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping

Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping

Different Algorithms for Obtaining Upper Bounds to Multivariate Normal Areas Outside of Origin Centered Rectangles Using Joint Marginal Probabilities

UniNovo : A Universal Tool for de Novo Peptide Sequencing

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