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	<title>Comments on: Exotic Probabilities</title>
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		<title>By: Marc Hamann</title>
		<link>http://www.arsmathematica.net/2005/08/09/exotic-probabilities/#comment-109</link>
		<dc:creator><![CDATA[Marc Hamann]]></dc:creator>
		<pubDate>Sat, 13 Aug 2005 02:08:13 +0000</pubDate>
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		<description><![CDATA[Maybe you should have gone for:

&quot;Frequentists?  How often do you see those?&quot;]]></description>
		<content:encoded><![CDATA[<p>Maybe you should have gone for:</p>
<p>&#8220;Frequentists?  How often do you see those?&#8221;</p>
]]></content:encoded>
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		<title>By: Charlie (Colorado)</title>
		<link>http://www.arsmathematica.net/2005/08/09/exotic-probabilities/#comment-105</link>
		<dc:creator><![CDATA[Charlie (Colorado)]]></dc:creator>
		<pubDate>Wed, 10 Aug 2005 00:34:05 +0000</pubDate>
		<guid isPermaLink="false">http://www.arsmathematica.net/?p=113#comment-105</guid>
		<description><![CDATA[Joke didn&#039;t work, huh?]]></description>
		<content:encoded><![CDATA[<p>Joke didn&#8217;t work, huh?</p>
]]></content:encoded>
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	<item>
		<title>By: sigfpe</title>
		<link>http://www.arsmathematica.net/2005/08/09/exotic-probabilities/#comment-104</link>
		<dc:creator><![CDATA[sigfpe]]></dc:creator>
		<pubDate>Tue, 09 Aug 2005 21:10:04 +0000</pubDate>
		<guid isPermaLink="false">http://www.arsmathematica.net/?p=113#comment-104</guid>
		<description><![CDATA[Is anyone in the world &lt;em&gt;not&lt;/em&gt; first taught probability theory from a frequentist perspective?]]></description>
		<content:encoded><![CDATA[<p>Is anyone in the world <em>not</em> first taught probability theory from a frequentist perspective?</p>
]]></content:encoded>
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	<item>
		<title>By: Charlie (Colorado)</title>
		<link>http://www.arsmathematica.net/2005/08/09/exotic-probabilities/#comment-103</link>
		<dc:creator><![CDATA[Charlie (Colorado)]]></dc:creator>
		<pubDate>Tue, 09 Aug 2005 19:16:16 +0000</pubDate>
		<guid isPermaLink="false">http://www.arsmathematica.net/?p=113#comment-103</guid>
		<description><![CDATA[A frequentist?  Are there any left?]]></description>
		<content:encoded><![CDATA[<p>A frequentist?  Are there any left?</p>
]]></content:encoded>
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		<title>By: PeterMcB</title>
		<link>http://www.arsmathematica.net/2005/08/09/exotic-probabilities/#comment-102</link>
		<dc:creator><![CDATA[PeterMcB]]></dc:creator>
		<pubDate>Tue, 09 Aug 2005 18:45:32 +0000</pubDate>
		<guid isPermaLink="false">http://www.arsmathematica.net/?p=113#comment-102</guid>
		<description><![CDATA[Such exotic variations of probability theory are not its only rivals -- the Kolmogorov axioms for probability theory (KPT) (using real numbers) are not uncontested, although a person could study mathematical statistics for many years before learning this (as I know from personal experience).   Most statisticians seem remarkably resistant to teaching alternatives to KPT. 

Although the arguments with the standard approach to PT go back to its earliest days (the decade around 1665), and have been repeated in each century since, in modern times the main criticisms have come from researchers in Artificial Intelligence.   KPT does not adequately or intuitively represent all forms of uncertainty, in particular, uncertainty about uncertainty.  As a consequence, Possibility theory and Dempster-Shafer Theory have arisen as alternatives to KPT.  Although many of these alternative approaches can be shown to be formally equivalent to second- or higher-order versions of KPT (eg, they involve random variables distributed according to functions with parameters which are themselves random variables), humans typically find them more intuitive than KPT.]]></description>
		<content:encoded><![CDATA[<p>Such exotic variations of probability theory are not its only rivals &#8212; the Kolmogorov axioms for probability theory (KPT) (using real numbers) are not uncontested, although a person could study mathematical statistics for many years before learning this (as I know from personal experience).   Most statisticians seem remarkably resistant to teaching alternatives to KPT. </p>
<p>Although the arguments with the standard approach to PT go back to its earliest days (the decade around 1665), and have been repeated in each century since, in modern times the main criticisms have come from researchers in Artificial Intelligence.   KPT does not adequately or intuitively represent all forms of uncertainty, in particular, uncertainty about uncertainty.  As a consequence, Possibility theory and Dempster-Shafer Theory have arisen as alternatives to KPT.  Although many of these alternative approaches can be shown to be formally equivalent to second- or higher-order versions of KPT (eg, they involve random variables distributed according to functions with parameters which are themselves random variables), humans typically find them more intuitive than KPT.</p>
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