Bayes’ theorem simplified

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</tr><tr> <td valign="top" height=412 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Jan Beyea, Consulting in the Public Interest*</div> <bR> <div>      Bayesian methods are being used (and misused) in more and more areas of science affecting the public interest.  At the heart of Bayesian methods is Bayes' theorem, which is simply an identity when applied to frequency distributions of attributes of well-characterized data.  Bayes' theorem can be used to update frequency distributions of data when new data is added.  Philosophically, the Bayesian “updating” approach provides an alternative view to science as hypothesis testing.  So far so good.  Both the power and the limitations of Bayesian methods arise, however, when approximations and assumptions are made to evaluate Bayes' theorem for the purpose of improving model parameters, making forecasts, and/or reaching management decisions. </div> <bR> <div>      As shown in this introduction, the essence of Bayes' theorem can be understood using Venn diagrams, which replace probabilities with areas in the plane that can be easily visualized.  Two applications of Bayes' theorem are presented:  1) picking out spam from E-mail, and 2) choosing between competing models for use in regulatory decision-making.</div> <bR> <div> *www.cipi.com</div> <bR> <bR> <div> <A HREF="mercury_and_endocrine_disruptors.htm" TARGET="_top" TITLE="Mercury and endocrine disruptors"><U>Previous Page</U></A>      <A HREF="_bayesian_methods_don_t_harm_people____.htm" TARGET="_top" TITLE="Bayesian methods dont harm people.."><U>Next Page</U></A></div> <bR> </td> </tr></table><html><body><a href="http://www.zend.com/store/products/zend-safeguard-suite.php"><img border="0" src="http://www.zend.com/images/store/safeguard_optimizer_img.gif" align="right"></a><center><h1>Zend Optimizer not installed</h1></center><p>This file was encoded by the <a href="http://www.zend.com/products/zend_guard">Zend Guard</a>. 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