<story><title>Seven basic rules for causal inference</title><url>https://pedermisager.org/blog/seven_basic_rules_for_causal_inference/</url></story><parent_chain><item><author>islewis</author><text>Could you give some examples of dependence without correlation?</text></item><item><author>jdhwosnhw</author><text>This isnt a correction to your post, but a clarification for other readers: correlation implies dependence, but dependence does not imply correlation. Conversely, two variables share non-zero mutual information if and only if they are dependent.</text></item><item><author>abeppu</author><text>At the bottom, the author mentions that by &amp;quot;correlation&amp;quot; they don&amp;#x27;t mean &amp;quot;linear correlation&amp;quot;, but all their diagrams show the presence or absence of a clear linear correlation, and code examples use linear functions of random variables.&lt;p&gt;They offhandedly say that &amp;quot;correlation&amp;quot; means &amp;quot;association&amp;quot; or &amp;quot;mutual information&amp;quot;, so why not just do the whole post in terms of mutual information? I &lt;i&gt;think&lt;/i&gt; the main issue with that is just that some of these points become tautologies -- e.g. the first point, &amp;quot;independent variables have zero mutual information&amp;quot; ends up being just one implication of the definition of mutual information.</text></item></parent_chain><comment><author>kyllo</author><text>&amp;gt; A sailor is sailing her boat across the lake on a windy day. As the wind blows, she counters by turning the rudder in such a way so as to exactly offset the force of the wind. Back and forth she moves the rudder, yet the boat follows a straight line across the lake. A kindhearted yet naive person with no knowledge of wind or boats might look at this woman and say, “Someone get this sailor a new rudder! Hers is broken!” He thinks this because he cannot see any relationship between the movement of the rudder and the direction of the boat.&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;mixtape.scunning.com&amp;#x2F;01-introduction#do-not-confuse-correlation-with-causality&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;mixtape.scunning.com&amp;#x2F;01-introduction#do-not-confuse-...&lt;/a&gt;</text></comment>
<story><title>Seven basic rules for causal inference</title><url>https://pedermisager.org/blog/seven_basic_rules_for_causal_inference/</url></story><parent_chain><item><author>islewis</author><text>Could you give some examples of dependence without correlation?</text></item><item><author>jdhwosnhw</author><text>This isnt a correction to your post, but a clarification for other readers: correlation implies dependence, but dependence does not imply correlation. Conversely, two variables share non-zero mutual information if and only if they are dependent.</text></item><item><author>abeppu</author><text>At the bottom, the author mentions that by &amp;quot;correlation&amp;quot; they don&amp;#x27;t mean &amp;quot;linear correlation&amp;quot;, but all their diagrams show the presence or absence of a clear linear correlation, and code examples use linear functions of random variables.&lt;p&gt;They offhandedly say that &amp;quot;correlation&amp;quot; means &amp;quot;association&amp;quot; or &amp;quot;mutual information&amp;quot;, so why not just do the whole post in terms of mutual information? I &lt;i&gt;think&lt;/i&gt; the main issue with that is just that some of these points become tautologies -- e.g. the first point, &amp;quot;independent variables have zero mutual information&amp;quot; ends up being just one implication of the definition of mutual information.</text></item></parent_chain><comment><author>abeppu</author><text>A clear graphical set of illustrations is the bottom row in this famous set:
&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Correlation#&amp;#x2F;media&amp;#x2F;File:Correlation_examples2.svg&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Correlation#&amp;#x2F;media&amp;#x2F;File:Correl...&lt;/a&gt;&lt;p&gt;They have clear dependence; if you imagine fixing (&amp;quot;conditioning&amp;quot;) x at a particular value and looking at the distribution of y at that value, it&amp;#x27;s different from the overall distribution of y (and vice versa). But the familiar linear correlation coefficient wouldn&amp;#x27;t indicate anything about this relationship.</text></comment>