BibSonomy publications for /http://www.bibsonomy.org/BibSonomy RSS feed for /2015-02-28T02:58:26+01:00The Shape of Differential Geometry in Geometric Calculushttp://www.bibsonomy.org/bibtex/27ed59d0c8a79117a36d27ddf2bf7322c/wolftypewolftype2015-02-27T22:52:23+01:00geometriccalculus <span class="authorEditorList"><a href="/author/Hestenes">David Hestenes</a>. </span><em>Guide to Geometric Algebra in Practice, </em><em>Springer London, </em>(<em>2011</em>)Fri Feb 27 22:52:23 CET 2015Guide to Geometric Algebra in Practice393-410The Shape of Differential Geometry in Geometric Calculus2011geometriccalculus We review the foundations for coordinate-free differential geometry in The Shape of Differential Geometry in Geometric Calculus - SpringerMultivector calculushttp://www.bibsonomy.org/bibtex/2f9e91f97fe99b047cf7161a6cd2f9625/wolftypewolftype2015-02-27T22:51:19+01:00geometricalgebra geometriccalculus <span class="authorEditorList"><a href="/author/Hestenes">David Hestenes</a>. </span><em>Journal of Mathematical Analysis and Applications - J MATH ANAL APPL</em> <em>24(2):313-325</em> (<em>1968</em>)Fri Feb 27 22:51:19 CET 2015Journal of Mathematical Analysis and Applications - J MATH ANAL APPL2313-325Multivector calculus241968geometricalgebra geometriccalculus Multivector calculus - ResearchGateWishart Generator Distributionhttp://www.bibsonomy.org/bibtex/2303357eb0a0eca4f4b073dedbb942e25/shabbychefshabbychef2015-02-27T20:54:42+01:00distributions multivariate statistics wishart <span class="authorEditorList"><a href="/author/Bekker">A. Bekker</a>, <a href="/author/Arashi">M. Arashi</a>, and <a href="/author/van+Niekerk">J. van Niekerk</a>. </span>(<em>2015</em>)<em>cite arxiv:1502.07300Comment: 22 pages.</em>Fri Feb 27 20:54:42 CET 2015cite arxiv:1502.07300Comment: 22 pagesWishart Generator Distribution2015distributions multivariate statistics wishart The Wishart distribution and its generalizations are among the most prominent
probability distributions in multivariate statistical analysis, arising
naturally in applied research and as a basis for theoretical models. In this
paper, we generalize the Wishart distribution utilizing a different approach
that leads to the Wishart generator distribution with the Wishart distribution
as a special case. It is not restricted, however some special cases are
exhibited. Important statistical characteristics of the Wishart generator
distribution are derived from the matrix theory viewpoint. Estimation is also
touched upon as a guide for further research from the classical approach as
well as from the Bayesian paradigm. The paper is concluded by giving
applications of two special cases of this distribution in calculating the
product of beta functions and astronomy.Wishart Generator DistributionOn Online Control of False Discovery Ratehttp://www.bibsonomy.org/bibtex/23763a6b1f2d0a5e17f001a53ed525ff4/shabbychefshabbychef2015-02-27T20:54:29+01:00FDR online statistics <span class="authorEditorList"><a href="/author/Javanmard">Adel Javanmard</a>, and <a href="/author/Montanari">Andrea Montanari</a>. </span>(<em>2015</em>)<em>cite arxiv:1502.06197Comment: 30 pages, 6 figures.</em>Fri Feb 27 20:54:29 CET 2015cite arxiv:1502.06197Comment: 30 pages, 6 figuresOn Online Control of False Discovery Rate2015FDR online statistics Multiple hypotheses testing is a core problem in statistical inference and
arises in almost every scientific field. Given a sequence of null hypotheses
$\mathcal{H}(n) = (H_1,\dotsc, H_n)$, Benjamini and
Hochberg~\cite{benjamini1995controlling} introduced the false discovery rate
(FDR) criterion, which is the expected proportion of false positives among
rejected null hypotheses, and proposed a testing procedure that controls FDR
below a pre-assigned significance level. They also proposed a different
criterion, called mFDR, which does not control a property of the realized set
of tests; rather it controls the ratio of expected number of false discoveries
to the expected number of discoveries.
In this paper, we propose two procedures for multiple hypotheses testing that
we will call "LOND" and "LORD". These procedures control FDR and mFDR in an
\emph{online manner}. Concretely, we consider an ordered --possibly infinite--
sequence of null hypotheses $\mathcal{H} = (H_1,H_2,H_3,\dots )$ where, at each
step $i$, the statistician must decide whether to reject hypothesis $H_i$
having access only to the previous decisions. To the best of our knowledge, our
work is the first that controls FDR in this setting. This model was introduced
by Foster and Stine~\cite{alpha-investing} whose alpha-investing rule only
controls mFDR in online manner.
In order to compare different procedures, we develop lower bounds on the
total discovery rate under the mixture model and prove that both LOND and LORD
have nearly linear number of discoveries. We further propose adjustment to LOND
to address arbitrary correlation among the $p$-values. Finally, we evaluate the
performance of our procedures on both synthetic and real data comparing them
with alpha-investing rule, Benjamin-Hochberg method and a Bonferroni procedure.On Online Control of False Discovery Ratedigitalricheshttp://www.bibsonomy.org/bibtex/2435561e93c098704657baae4c69f371a/digitalrichesdigitalriches2015-02-27T20:44:50+01:00digitalriches <span class="authorEditorList"><a href="/author/the+search+engines+with+video+marketing">Dominate the search engines with video marketing</a>, and <a href="/author/generate+highly+targeted+traffic+to+your+products+or+services."> generate highly targeted traffic to your products or services.</a>. </span><em>digitalriches</em> <em>digitalriches(digitalriches):digitalriches</em> (<em>January 2015</em>)<em>digitalriches.</em>Fri Feb 27 20:44:50 CET 2015digitalrichesjanuarydigitalrichesdigitalrichesdigitalrichesdigitalriches
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