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Related topics

Suppose

resulting from the $s$ tests are ordered such that $p(1) \le p(2) \le \cdots \le p(s)$. Here we might restrict our attention to those $3\sigma$ or $4\sigma$ detections.

Now we find $$d = \max_{1 \le k \le s}\{k: p(k) \le \alpha \cdot k/s\},$$ then rejecting the null hypotheses (identify detections) corresponding to $p(1), \cdots, p(d)$ provides $FDR \le \alpha$.

Note that only pixels with $p$-values less than $\alpha$ matter. $% Error during latex2img: ERROR: problems during latex INPUT: \documentclass[fleqn,12pt]{article} \usepackage{amsmath} \usepackage[normal]{xcolor} \setlength{\mathindent}{0cm} \definecolor{teal}{rgb}{0,0.5,0.5} \definecolor{navy}{rgb}{0,0,0.5} \definecolor{aqua}{rgb}{0,1,1} \definecolor{lime}{rgb}{0,1,0} \definecolor{maroon}{rgb}{0.5,0,0} \definecolor{silver}{gray}{0.75} \usepackage{latexsym} \begin{document} \pagestyle{empty} \pagecolor{white} { \color{black} \begin{math}\displaystyle$0 < \alpha< 1$is the {\it a priori} error rate (similar to significance level) set, and suppose the$p$-values\end{math} } \clearpage \end{document} STDERR: This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (/tmp/BowPLY7fi_/co7FKxAZHC LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/fleqn.clo) (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/xcolor/xcolor.sty (/usr/share/texmf/tex/latex/config/color.cfg) (/usr/share/texmf/tex/latex/graphics/dvips.def)) (/usr/share/texmf/tex/latex/base/latexsym.sty) No file co7FKxAZHC.aux. (/usr/share/texmf/tex/latex/base/ulasy.fd) ! Missing$ inserted.

$l.17 \begin{math}\displaystyle$0 < \alpha
< 1$is the {\it a priori} error r... ! LaTeX Error: Bad math environment delimiter. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.17 ... set, and suppose the$p\$-values\end{math}

[1] (./co7FKxAZHC.aux) )
(see the transcript file for additional information)
Output written on co7FKxAZHC.dvi (1 page, 592 bytes).
Transcript written on co7FKxAZHC.log.
Topic attachments
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doc im811sy.doc manage 44.5 K 2008-01-07 - 15:00 UnknownUser
Topic revision: r8 - 2009-10-15, UnknownUser

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