Document Zbl 1544.62078

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1544.62078 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/?q=rj%3A21+se%3A7120+sw%3Arethinking"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="rj:21 se:7120 sw:rethinking" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/kelter.riko" title="Author Profile">Kelter, Riko</a></div> <h2 class="title"> <strong>Bayesian and frequentist testing for differences between two groups with parametric and nonparametric two-sample tests.</strong> <i>(English)</i> <a class="label nowrap" href="/1544.62078">Zbl 1544.62078</a> </h2> <div class="source"> <a href="/serials/7120" title="Journal Profile">Wiley Interdiscip. Rev., WIREs Comput. Stat.</a> <a href="/?q=in%3A517036" title="Articles in this Issue">13, No. 6, Article ID e1523, 29 p. (2021)</a>. </div> <div class="abstract"></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7910760">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-08" title="MSC2020">62-08</a> </td> <td class="space"> Computational methods for problems pertaining to statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ABayesian+two-sample+tests">Bayesian two-sample tests</a>; <a href="/?q=ut%3AMann-Whitney+%5C%28U%5C%29+test">Mann-Whitney $U$ test</a>; <a href="/?q=ut%3Anull+hypothesis+significance+testing">null hypothesis significance testing</a>; <a href="/?q=ut%3AStudent%27s+%5C%28t%5C%29-test">Student’s $t$-test</a>; <a href="/?q=ut%3Atesting+for+differences+between+two+groups">testing for differences between two groups</a></div> <div class="software"> <h3>Software:</h3><a href="/software/25139">rethinking</a>; <a href="/software/10200">Stan</a>; <a href="/software/8040">JAGS</a>; <a href="/software/771">R</a>; <a href="/software/33317">bayest</a>; <a href="/software/4351">CRAN</a>; <a href="/software/9311">bayess</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1544.62078" data-ciurl="/ci/07910760" data-biburl="/bibtex/07910760.bib" data-amsurl="/amsrefs/07910760.bib" data-xmlurl="/xml/07910760.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07910760.pdf" title="Zbl 1544.62078 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1002/wics.1523" aria-label="DOI for “Bayesian and frequentist testing for differences between two groups with parametric and nonparametric two-sample tests”" title="10.1002/wics.1523">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by-nc-nd/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nc.svg" alt="Creative Commons NC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nd.svg" alt="Creative Commons ND license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Benjamin, D. J.; Berger, J. O.; Johannesson, M.; Nosek, B. A.; Wagenmakers, E.‐J.; Berk, R.; Johnson, V. E., Redefine statistical significance, Nature Human Behaviour, 2, 6-10, 2018</td> </tr><tr> <td>[2]</td> <td class="space">Berger, J.; Brown, L.; Wolpert, R., A unified conditional frequentist and Bayesian test for fixed and sequential hypothesis testing, The Annals of Statistics, 22, 1787-1807, 1994 · <a href="/0824.62002" class="nowrap">Zbl 0824.62002</a></td> </tr><tr> <td>[3]</td> <td class="space">Berger, J. O., Could Fisher, Jeffreys and Neyman have agreed on testing?, Statistical Science, 18, 1-32, 2003 · <a href="/1048.62006" class="nowrap">Zbl 1048.62006</a></td> </tr><tr> <td>[4]</td> <td class="space">Berger, J. O.; Boukai, B.; Wang, Y., Unified frequentist and Bayesian testing of a precise hypothesis, Statistical Science, 12, 133-160, 1997 · <a href="/0955.62527" class="nowrap">Zbl 0955.62527</a></td> </tr><tr> <td>[5]</td> <td class="space">Berger, J. O.; Wolpert, R. L., The likelihood principle, 1988, Hayward, CA: Institute of Mathematical Statistics</td> </tr><tr> <td>[6]</td> <td class="space">Carpenter, B.; Guo, J.; Hoffman, M. D.; Brubaker, M.; Gelman, A.; Lee, D.; Betancourt, M., Stan: A probabilistic programming language, Journal of Statistical Software, 76, 1-32, 2017</td> </tr><tr> <td>[7]</td> <td class="space">Casella, G.; Berger, R. L., Statistical inference, 2002, Stamford, CT: Thomson Learning</td> </tr><tr> <td>[8]</td> <td class="space">Cohen, J., Statistical power analysis for the behavioral sciences. 2nd ed., 1988, Hillsdale, NJ: Routledge · <a href="/0747.62110" class="nowrap">Zbl 0747.62110</a></td> </tr><tr> <td>[9]</td> <td class="space">Colquhoun, D., The reproducibility of research and the misinterpretation of p‐values, Royal Society Open Science, 4, 171085, 2017 · <a href="https://doi.org/10.1098/rsos.171085" class="nowrap">doi:10.1098/rsos.171085</a></td> </tr><tr> <td>[10]</td> <td class="space">Cox, D., Some problems connected with statistical inference, The Annals of Mathematical Statistics, 29, 357-372, 1958 · <a href="/0088.11702" class="nowrap">Zbl 0088.11702</a></td> </tr><tr> <td>[11]</td> <td class="space">Cumming, G., The new statistics: Why and how, Psychological Science, 25, 7-29, 2014</td> </tr><tr> <td>[12]</td> <td class="space">Escobar, M. D.; West, M., Bayesian density estimation and inference using mixtures, Journal of the American Statistical Association, 90, 577-588, 1995 · <a href="/0826.62021" class="nowrap">Zbl 0826.62021</a></td> </tr><tr> <td>[13]</td> <td class="space">Fisher, R. A., Statistical methods for research workers, 1925, Edinburgh, England: Oliver and Boyd, Hafner Publishing Company · <a href="/51.0414.08" class="nowrap">JFM 51.0414.08</a></td> </tr><tr> <td>[14]</td> <td class="space">Frühwirth‐Schnatter, S., Finite mixture and Markov switching models, 2006, Berlin: Springer · <a href="/1108.62002" class="nowrap">Zbl 1108.62002</a></td> </tr><tr> <td>[15]</td> <td class="space">Gabry, J.; Simpson, D.; Vehtari, A.; Betancourt, M.; Gelman, A., Visualization in Bayesian workflow, Journal of the Royal Statistical Society: Series A (Statistics in Society), 182, 389-402, 2019 · <a href="/07972646" class="nowrap">Zbl 07972646</a> · <a href="https://doi.org/10.1111/rssa.12378" class="nowrap">doi:10.1111/rssa.12378</a></td> </tr><tr> <td>[16]</td> <td class="space">Gelman, A.; Lee, D.; Guo, J., Stan: A probabilistic programming language for Bayesian inference, Journal of Educational and Behavioral Statistics, 40, 530-543, 2015 · <a href="https://doi.org/10.3102/1076998615606113" class="nowrap">doi:10.3102/1076998615606113</a></td> </tr><tr> <td>[17]</td> <td class="space">Geman, S.; Geman, D., Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI‐6, 721-741, 1984 · <a href="/0573.62030" class="nowrap">Zbl 0573.62030</a></td> </tr><tr> <td>[18]</td> <td class="space">Goddard, S. D.; Johnson, V. E., Restricted most powerful Bayesian tests for linear models, Scandinavian Journal of Statistics, 43, 1162-1177, 2016 · <a href="/1373.62353" class="nowrap">Zbl 1373.62353</a> · <a href="https://doi.org/10.1111/sjos.12235" class="nowrap">doi:10.1111/sjos.12235</a></td> </tr><tr> <td>[19]</td> <td class="space">Gönen, M.; Johnson, W. O.; Lu, Y.; Westfall, P. H., The Bayesian two‐sample t test, The American Statistician, 59, 252-257, 2005</td> </tr><tr> <td>[20]</td> <td class="space">Goodman, S. N., Toward evidence‐based medical statistics. 2: The Bayes factor, Annals of Internal Medicine, 130, 1005-1013, 1999 · <a href="https://doi.org/10.7326/0003-4819-130-12-199906150-00019" class="nowrap">doi:10.7326/0003-4819-130-12-199906150-00019</a></td> </tr><tr> <td>[21]</td> <td class="space">Gronau, Q. F.; Ly, A.; Wagenmakers, E.‐J., Informed Bayesian t‐tests, The American Statistician, 00, 1-7, 2019</td> </tr><tr> <td>[22]</td> <td class="space">Held, L.; Ott, M., How the maximal evidence of p‐values against point null hypotheses depends on sample size, The American Statistician, 70, 335-341, 2016 · <a href="/07665893" class="nowrap">Zbl 07665893</a> · <a href="https://doi.org/10.1080/00031305.2016.1209128" class="nowrap">doi:10.1080/00031305.2016.1209128</a></td> </tr><tr> <td>[23]</td> <td class="space">Held, L.; Ott, M., On p‐values and Bayes factors, Annual Review of Statistics and its Application, 5, 393-419, 2018 · <a href="https://doi.org/10.1146/annurev-statistics-031017-100307" class="nowrap">doi:10.1146/annurev-statistics-031017-100307</a></td> </tr><tr> <td>[24]</td> <td class="space">Held, L.; Sabanés Bové, D., Applied statistical inference, 2014, Berlin, Heidelberg: Springer · <a href="/1281.62005" class="nowrap">Zbl 1281.62005</a></td> </tr><tr> <td>[25]</td> <td class="space">Hoffman, M. D.; Gelman, A., The no‐U‐turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research, 15, 1351-1381, 2014 · <a href="/1319.60150" class="nowrap">Zbl 1319.60150</a></td> </tr><tr> <td>[26]</td> <td class="space">Ioannidis, J. P., Contradicted and initially stronger effects in highly cited clinical research, Journal of the American Medical Association, 294, 218-228, 2005 · <a href="https://doi.org/10.1001/jama.294.2.218" class="nowrap">doi:10.1001/jama.294.2.218</a></td> </tr><tr> <td>[27]</td> <td class="space">Jeffreys, H., Theory of probability. 1st ed., 1939, Oxford, England: The Clarendon Press · <a href="/65.0546.04" class="nowrap">JFM 65.0546.04</a></td> </tr><tr> <td>[28]</td> <td class="space">Jeffreys, H., Theory of probability. 3rd ed., 1961, Oxford, England: Oxford University Press · <a href="/0116.34904" class="nowrap">Zbl 0116.34904</a></td> </tr><tr> <td>[29]</td> <td class="space">Kass, R. E.; Raftery, A. E., Bayes factors, Journal of the American Statistical Association, 90, 773-795, 1995 · <a href="/0846.62028" class="nowrap">Zbl 0846.62028</a></td> </tr><tr> <td>[30]</td> <td class="space">Kelter, R., bayest: Effect size targeted Bayesian two‐sample t‐tests via Markov chain Monte Carlo in Gaussian mixture models, 2019, Comprehensive R Archive Network</td> </tr><tr> <td>[31]</td> <td class="space">Kelter, R., Analysis of Bayesian posterior significance and effect size indices for the two‐sample t‐test to support reproducible medical research, BMC Medical Research Methodology, 20, 88, 2020</td> </tr><tr> <td>[32]</td> <td class="space">Kelter, R., Bayesian alternatives to null hypothesis significance testing in biomedical research: A non‐technical introduction to Bayesian inference with JASP, BMC Medical Research Methodology, 20, 2020 · <a href="https://doi.org/10.1186/s12874-020-00980-6" class="nowrap">doi:10.1186/s12874-020-00980-6</a></td> </tr><tr> <td>[33]</td> <td class="space">Kelter, R., bayest: An R package for effect‐size targeted Bayesian two‐sample t‐tests, Journal of Open Research Software, 8, 1, 1-4, 2020 · <a href="https://doi.org/10.5334/jors.290" class="nowrap">doi:10.5334/jors.290</a></td> </tr><tr> <td>[34]</td> <td class="space">Kelter, R.; Kramer, M.; Brinda, T., Teachers perspectives on object‐oriented programming environments for secondary education, Proceedings of the IFIP TC3 open conference on comp, 2018, Cham, Switzerland: International Federation for Information Processing (IFIP)</td> </tr><tr> <td>[35]</td> <td class="space">Kruschke, J. K., Bayesian estimation supersedes the t‐test, Journal of Experimental Psychology: General, 142, 573-603, 2013</td> </tr><tr> <td>[36]</td> <td class="space">Kruschke, J. K., Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. 2nd ed., 2015, Oxford, England: Academic Press</td> </tr><tr> <td>[37]</td> <td class="space">Kruschke, J. K., Rejecting or accepting parameter values in Bayesian estimation, Advances in Methods and Practices in Psychological Science, 1, 2, 270-280, 2018</td> </tr><tr> <td>[38]</td> <td class="space">Kruschke, J. K.; Liddell, T., The Bayesian new statistics: Hypothesis testing, estimation, meta‐analysis, and power analysis from a Bayesian perspective, Psychonomic Bulletin and Review, 25, 178-206, 2018</td> </tr><tr> <td>[39]</td> <td class="space">Kruschke, J. K.; Liddell, T. M., The Bayesian new statistics: From a Bayesian perspective, 1-28, 2017, Berlin: Springer</td> </tr><tr> <td>[40]</td> <td class="space">Lee, M. D.; Wagenmakers, E.‐J., Bayesian cognitive modeling: A practical course, 2013, Amsterdam, Netherlands: Cambridge University Press</td> </tr><tr> <td>[41]</td> <td class="space">Lehmann, E. L. E. L.; Casella, G., Theory of point estimation, 1998, New York, NY: Springer · <a href="/0916.62017" class="nowrap">Zbl 0916.62017</a></td> </tr><tr> <td>[42]</td> <td class="space">Liang, F.; Paulo, R.; Molina, G.; Clyde, M. A.; Berger, J. O., Mixtures of g priors for Bayesian variable selection, Journal of the American Statistical Association, 103, 410-423, 2008 · <a href="/1335.62026" class="nowrap">Zbl 1335.62026</a></td> </tr><tr> <td>[43]</td> <td class="space">Lindley, D., A statistical paradox, Biometrika, 44, 187-192, 1957 · <a href="/0080.12801" class="nowrap">Zbl 0080.12801</a></td> </tr><tr> <td>[44]</td> <td class="space">Makowski, D.; Ben‐Shachar, M. S.; Chen, S. H. A.; Lüdecke, D., Indices of effect existence and significance in the Bayesian framework, Frontiers in Psychology, 10, 2767, 2019 · <a href="https://doi.org/10.3389/fpsyg.2019.02767/full" class="nowrap">doi:10.3389/fpsyg.2019.02767/full</a></td> </tr><tr> <td>[45]</td> <td class="space">Marin, J.‐M.; Robert, C., Bayesian essentials with R, 2014, New York, NY: Springer · <a href="/1380.62005" class="nowrap">Zbl 1380.62005</a></td> </tr><tr> <td>[46]</td> <td class="space">Matthews, R.; Wasserstein, R.; Spiegelhalter, D., The ASA’s p‐value statement, one year on, Significance, 14, 38-41, 2017 · <a href="https://doi.org/10.1111/j.1740-9713.2017.01021.x" class="nowrap">doi:10.1111/j.1740-9713.2017.01021.x</a></td> </tr><tr> <td>[47]</td> <td class="space">Matzke, D.; Nieuwenhuis, S.; van Rijn, H.; Slagter, H. A.; van der Molen, M. W.; Wagenmakers, E.‐J., The effect of horizontal eye movements on free recall: A preregistered adversarial collaboration, Journal of Experimental Psychology: General, 144, e1-e15, 2015 · <a href="https://doi.org/10.1037/xge0000038" class="nowrap">doi:10.1037/xge0000038</a></td> </tr><tr> <td>[48]</td> <td class="space">McElreath, R., Statistical rethinking: A Bayesian course with examples in R and Stan, 2016, Boca Raton, FL: Chapman & Hall, CRC Press · <a href="https://doi.org/10.3102/1076998616659752" class="nowrap">doi:10.3102/1076998616659752</a></td> </tr><tr> <td>[49]</td> <td class="space">McElreath, R.; Smaldino, P. E., Replication, communication, and the population dynamics of scientific discovery, PLoS One, 10, 1-16, 2015</td> </tr><tr> <td>[50]</td> <td class="space">Mills, J., 2017</td> </tr><tr> <td>[51]</td> <td class="space">Neyman, A. J.; Pearson, E. S., On the use and interpretation of certain test criteria for purposes of statistical inference: Part I, Biometrika, 20, 175-240, 1928 · <a href="/54.0565.05" class="nowrap">JFM 54.0565.05</a></td> </tr><tr> <td>[52]</td> <td class="space">Neyman, J., “Inductive behavior” as a basic concept of philosophy of science, Review of the International Statistical Institute, 25, 7-22, 1957 · <a href="/0087.24404" class="nowrap">Zbl 0087.24404</a></td> </tr><tr> <td>[53]</td> <td class="space">Neyman, J.; Pearson, E. S., On the problem of the most efficient tests of statistical hypotheses, Philosophical Transactions of the Royal Society A, 231, 289-337, 1933 · <a href="/59.1163.02" class="nowrap">JFM 59.1163.02</a></td> </tr><tr> <td>[54]</td> <td class="space">Neyman, J.; Pearson, E. S., Contributions to the theory of testing statistical hypotheses, Statistical Research Memoirs, 1, 1-37, 1936 · <a href="/62.0609.02" class="nowrap">JFM 62.0609.02</a></td> </tr><tr> <td>[55]</td> <td class="space">Nuijten, M. B.; Hartgerink, C. H.; van Assen, M. A.; Epskamp, S.; Wicherts, J. M., The prevalence of statistical reporting errors in psychology (1985-2013), Behavior Research Methods, 48, 1205-1226, 2016</td> </tr><tr> <td>[56]</td> <td class="space">Pereira, C. A. d. B.; Stern, J. M., Evidence and credibility: Full Bayesian significance test for precise hypotheses, Entropy, 1, 99-110, 1999 · <a href="/0993.62028" class="nowrap">Zbl 0993.62028</a></td> </tr><tr> <td>[57]</td> <td class="space">Pereira, C. A. d. B.; Stern, J. M.; Wechsler, S., Can a significance test be genuinely Bayesian?, Bayesian Analysis, 3, 79-100, 2008 · <a href="/1330.62049" class="nowrap">Zbl 1330.62049</a></td> </tr><tr> <td>[58]</td> <td class="space">Quintana, D. S.; Williams, D. R., Bayesian alternatives for common null‐hypothesis significance tests in psychiatry: A non‐technical guide using JASP, BMC Psychiatry, 18, 2018</td> </tr><tr> <td>[59]</td> <td class="space">R Core Team, 2020</td> </tr><tr> <td>[60]</td> <td class="space">Richardson, S.; Green, P., On Bayesian analysis of mixtures with an unknown number of components, Journal of the Royal Statistical Society: Series B, 59, 731-792, 1997 · <a href="/0891.62020" class="nowrap">Zbl 0891.62020</a></td> </tr><tr> <td>[61]</td> <td class="space">Robert, C. P., The expected demise of the Bayes factor, Journal of Mathematical Psychology, 72, 33-37, 2016 · <a href="/1357.62127" class="nowrap">Zbl 1357.62127</a></td> </tr><tr> <td>[62]</td> <td class="space">Rochon, J.; Gondan, M.; Kieser, M., To test or not to test: Preliminary assessment of normality when comparing two independent samples, BMC Medical Research Methodology, 12, 1-11, 2012</td> </tr><tr> <td>[63]</td> <td class="space">Rouder, J. N.; Speckman, P. L.; Sun, D.; Morey, R. D.; Iverson, G., Bayesian t tests for accepting and rejecting the null hypothesis, Psychonomic Bulletin and Review, 16, 225-237, 2009</td> </tr><tr> <td>[64]</td> <td class="space">Samaniego, F. J., Springer series in statistics, 2010, New York, NY: Springer New York · <a href="/1204.62028" class="nowrap">Zbl 1204.62028</a> · <a href="https://doi.org/10.1007/978-1-4419-5941-6" class="nowrap">doi:10.1007/978-1-4419-5941-6</a></td> </tr><tr> <td>[65]</td> <td class="space">Tanner, M.; Wong, W. H., The calculation of posterior distributions by data augmentation, Journal of the American Statistical Association, 82, 528-540, 1987 · <a href="/0619.62029" class="nowrap">Zbl 0619.62029</a></td> </tr><tr> <td>[66]</td> <td class="space">Topolinski, S.; Sparenberg, P., Turning the hands of time, Social Psychological and Personality Science, 3, 308-314, 2012 · <a href="https://doi.org/10.1177/1948550611419266" class="nowrap">doi:10.1177/1948550611419266</a></td> </tr><tr> <td>[67]</td> <td class="space">van Doorn, J.; Ly, A.; Marsman, M.; Wagenmakers, E.‐J., Bayesian rank‐based hypothesis testing for the rank sum test, the signed rank test, and Spearman’s rho, Journal of Applied Statistics, 1-23, 2020 · <a href="/1521.62510" class="nowrap">Zbl 1521.62510</a></td> </tr><tr> <td>[68]</td> <td class="space">Wagenmakers, E.‐J.; Beek, T.; Rotteveel, M.; Gierholz, A.; Matzke, D.; Steingroever, H.; Pinto, Y., Turning the hands of time again: A purely confirmatory replication study and a Bayesian analysis, Frontiers in Psychology, 6, 494, 2015 · <a href="https://doi.org/10.3389/fpsyg.2015.00494" class="nowrap">doi:10.3389/fpsyg.2015.00494</a></td> </tr><tr> <td>[69]</td> <td class="space">Wagenmakers, E.‐J.; Lodewyckx, T.; Kuriyal, H.; Grasman, R., Bayesian hypothesis testing for psychologists: A tutorial on the Savage-Dickey method, Cognitive Psychology, 60, 158-189, 2010</td> </tr><tr> <td>[70]</td> <td class="space">Wang, M.; Liu, G., A simple two‐sample Bayesian t‐test for hypothesis testing, American Statistician, 70, 195-201, 2016 · <a href="/07665872" class="nowrap">Zbl 07665872</a></td> </tr><tr> <td>[71]</td> <td class="space">Wasserstein, R. L.; Lazar, N. A., The ASA’s statement on p‐values: Context, process, and purpose, The American Statistician, 70, 129-133, 2016 · <a href="/07665862" class="nowrap">Zbl 07665862</a></td> </tr><tr> <td>[72]</td> <td class="space">Wasserstein, R. L.; Schirm, A. L.; Lazar, N. A., Moving to a world beyond “p < 0.05”, The American Statistician, 73, 1-19, 2019 · <a href="/07588180" class="nowrap">Zbl 07588180</a></td> </tr><tr> <td>[73]</td> <td class="space">Wetzels, R.; Raaijmakers, J. G.; Jakab, E.; Wagenmakers, E.‐J., How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test, Psychonomic Bulletin and Review, 16, 752-760, 2009</td> </tr><tr> <td>[74]</td> <td class="space">Wilcox, R. R., How many discoveries have been lost by ignoring modern statistical methods?, American Psychologist, 53, 300-314, 1998</td> </tr><tr> <td>[75]</td> <td class="space">Yuan, Y.; Johnson, V. E., Bayesian hypothesis tests using nonparametric statistics, Statistica Sinica, 18, 1185-1200, 2008 · <a href="/1149.62038" class="nowrap">Zbl 1149.62038</a></td> </tr><tr> <td>[76]</td> <td class="space">Zellner, A., Introduction, Bayesian analysis in econometrics and statistics: Essays in honor of Harold Jeffreys, 1980, Amsterdam, Netherlands: North‐Holland Pub. Co. · <a href="/0515.62098" class="nowrap">Zbl 0515.62098</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1544.62078 - zbMATH Open