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	<title>neuroscience &#8211; Mathemafrica</title>
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		<title>You&#8217;re (probably) a Bayesian &#8211; whether you like it or not!</title>
		<link>http://www.mathemafrica.org/?p=12104</link>
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		<pubDate>Wed, 03 Feb 2016 14:02:49 +0000</pubDate>
		<dc:creator><![CDATA[Alex Antrobus]]></dc:creator>
				<category><![CDATA[English]]></category>
		<category><![CDATA[Fun]]></category>
		<category><![CDATA[Level: Simple]]></category>
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		<category><![CDATA[bayesian]]></category>
		<category><![CDATA[neuroscience]]></category>
		<category><![CDATA[probability]]></category>

		<guid isPermaLink="false">http://www.mathemafrica.org/?p=12104</guid>
		<description><![CDATA[<p>Statisticians have long been separated into two camps as to how they philosophically interpret their trade. These schools of thought are usually called <em>Frequentists</em> and <em>Bayesians</em>.</p>
<p>Frequentists believe that a probability, <img src="//s0.wp.com/latex.php?latex=p%5Cin%5B0%7E+1%5D+&#038;bg=ffffff&#038;fg=000&#038;s=0" alt="p&#92;in[0~ 1] " title="p&#92;in[0~ 1] " class="latex" />,   associated with a <em>specific</em> possible outcome of an observable occurrence or process, is simply telling you that, could you <em>observe</em> this occurrence (or process) infinitely many times, the fraction of such observations that would yield that <em>specific</em> outcome is <img src="//s0.wp.com/latex.php?latex=p&#038;bg=ffffff&#038;fg=000&#038;s=0" alt="p" title="p" class="latex" /> .  Using the age-old coin toss example: tossing the coin is the occurrence or process and recording a Heads or Tails are the two observation. The number 0.5  <img src="//s0.wp.com/latex.php?latex=%5Cleft%28P%28%5Ctext%7BTails%7D%29%3D0.5%3DP%28%5Ctext%7BHeads%7D%29%5Cright%29&#038;bg=ffffff&#038;fg=000&#038;s=0" alt="&#92;left(P(&#92;text{Tails})=0.5=P(&#92;text{Heads})&#92;right)" title="&#92;left(P(&#92;text{Tails})=0.5=P(&#92;text{Heads})&#92;right)" class="latex" /> tells a Frequentist that, in the pursuit of infinitely many coin tosses, the ratio of Heads recorded to the number of tosses performed asymptotically approaches 0.5. And that&#8217;s all! The value should not be interpreted as the most likely outcome for the next observation or sample taken from the process (though I&#8217;ve always wondered how a Frequentist would gamble&#8230;).&#8230;</p>]]></description>
				<content:encoded><![CDATA[<p>Statisticians have long been separated into two camps as to how they philosophically interpret their trade. These schools of thought are usually called <em>Frequentists</em> and <em>Bayesians</em>.</p>
<p>Frequentists believe that a probability, <img src="//s0.wp.com/latex.php?latex=p%5Cin%5B0%7E+1%5D+&#038;bg=ffffff&#038;fg=000&#038;s=0" alt="p&#92;in[0~ 1] " title="p&#92;in[0~ 1] " class="latex" />,   associated with a <em>specific</em> possible outcome of an observable occurrence or process, is simply telling you that, could you <em>observe</em> this occurrence (or process) infinitely many times, the fraction of such observations that would yield that <em>specific</em> outcome is <img src="//s0.wp.com/latex.php?latex=p&#038;bg=ffffff&#038;fg=000&#038;s=0" alt="p" title="p" class="latex" /> .  Using the age-old coin toss example: tossing the coin is the occurrence or process and recording a Heads or Tails are the two observation. The number 0.5  <img src="//s0.wp.com/latex.php?latex=%5Cleft%28P%28%5Ctext%7BTails%7D%29%3D0.5%3DP%28%5Ctext%7BHeads%7D%29%5Cright%29&#038;bg=ffffff&#038;fg=000&#038;s=0" alt="&#92;left(P(&#92;text{Tails})=0.5=P(&#92;text{Heads})&#92;right)" title="&#92;left(P(&#92;text{Tails})=0.5=P(&#92;text{Heads})&#92;right)" class="latex" /> tells a Frequentist that, in the pursuit of infinitely many coin tosses, the ratio of Heads recorded to the number of tosses performed asymptotically approaches 0.5. And that&#8217;s all! The value should not be interpreted as the most likely outcome for the next observation or sample taken from the process (though I&#8217;ve always wondered how a Frequentist would gamble&#8230;).&hellip;</p>]]></content:encoded>
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		<title>The experience of mathematical beauty and its neural correlates</title>
		<link>http://www.mathemafrica.org/?p=11685</link>
		<comments>http://www.mathemafrica.org/?p=11685#respond</comments>
		<pubDate>Wed, 14 Oct 2015 12:07:46 +0000</pubDate>
		<dc:creator><![CDATA[Jonathan Shock]]></dc:creator>
				<category><![CDATA[English]]></category>
		<category><![CDATA[Level: intermediate]]></category>
		<category><![CDATA[News]]></category>
		<category><![CDATA[beauty]]></category>
		<category><![CDATA[neuroscience]]></category>
		<category><![CDATA[research]]></category>

		<guid isPermaLink="false">http://www.mathemafrica.org/?p=11685</guid>
		<description><![CDATA[<p>Check out a mathematics and neuroscience <a href="http://journal.frontiersin.org/article/10.3389/fnhum.2014.00068/full">paper here</a>, whose authors include Fields and Abel medalist <a href="https://en.wikipedia.org/wiki/Michael_Atiyah">Michael Atiyah</a>.</p>
<div id="attachment_11686" style="width: 679px" class="wp-caption aligncenter"><a href="http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png"><img class="wp-image-11686 size-large" src="http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?resize=669%2C458" alt="Untitled 2" srcset="http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?resize=300%2C205 300w, http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?resize=1024%2C701 1024w, http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?fit=1863%2C1276 1863w" sizes="(max-width: 669px) 100vw, 669px" data-recalc-dims="1" /></a><p class="wp-caption-text">http://journal.frontiersin.org/article/10.3389/fnhum.2014.00068/full published in frontiers in human neuroscience.</p></div>
<table class="rw-rating-table rw-ltr rw-left"><tr><td><nobr>How clear is this post?</nobr></td><td><div class="rw-left"><div class="rw-ui-container rw-class-blog-post rw-urid-116860" data-img="http://www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png"></div></div></td></tr></table>&#8230;]]></description>
				<content:encoded><![CDATA[<p>Check out a mathematics and neuroscience <a href="http://journal.frontiersin.org/article/10.3389/fnhum.2014.00068/full">paper here</a>, whose authors include Fields and Abel medalist <a href="https://en.wikipedia.org/wiki/Michael_Atiyah">Michael Atiyah</a>.</p>
<div id="attachment_11686" style="width: 679px" class="wp-caption aligncenter"><a href="http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png"><img class="wp-image-11686 size-large" src="http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?resize=669%2C458" alt="Untitled 2" srcset="http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?resize=300%2C205 300w, http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?resize=1024%2C701 1024w, http://i2.wp.com/www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png?fit=1863%2C1276 1863w" sizes="(max-width: 669px) 100vw, 669px" data-recalc-dims="1" /></a><p class="wp-caption-text">http://journal.frontiersin.org/article/10.3389/fnhum.2014.00068/full published in frontiers in human neuroscience.</p></div>
<table class="rw-rating-table rw-ltr rw-left"><tr><td><nobr>How clear is this post?</nobr></td><td><div class="rw-left"><div class="rw-ui-container rw-class-blog-post rw-urid-116860" data-img="http://www.mathemafrica.org/wp-content/uploads/2015/10/Untitled-2.png"></div></div></td></tr></table>&hellip;]]></content:encoded>
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