{"id":29,"date":"2006-10-15T12:00:22","date_gmt":"2006-10-15T20:00:22","guid":{"rendered":"http:\/\/www.mii.ucla.edu\/causality\/?p=39"},"modified":"2006-10-15T12:00:22","modified_gmt":"2006-10-15T20:00:22","slug":"the-validity-of-g-estimation","status":"publish","type":"post","link":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/2006\/10\/15\/the-validity-of-g-estimation\/","title":{"rendered":"The validity of G-estimation"},"content":{"rendered":"<p><font><strong>From a previous correspondence with <\/strong><\/font><font><strong>Eliezer S. Yudkowsky, Research Fellow, Singularity Institute         for Artificial Intelligence, Santa Clara, CA <\/strong><\/font><\/p>\n<p><font> The following paragraph appears on p. 103, shortly after eq. 3.63 in  my copy of <em>Causality<\/em>: <\/font><\/p>\n<p><font>&quot;To place this result in the context of our analysis in this chapter, we note  that the class of semi-Markovian models satisfying assumption (3.62)  corresponds to complete DAGs in which all arrowheads pointing to <em>X<sub>k<\/sub><\/em> originate  from observed variables.&quot; <\/font><\/p>\n<p><font>It looks to me like this is a sufficient, but not necessary, condition to  satisfy 3.62.  It appears to me that the necessary condition is that no  confounder exist between any <em>X<sub>i<\/sub><\/em> and <em>L<sub>j<\/sub><\/em>  with <em>i &lt; j<\/em> and that no confounder  exist between any <em>X<sub>i<\/sub><\/em> and the outcome variable <em>Y<\/em>.   However, a confounding arc between any <em>X<sub>i<\/sub><\/em> and  <em>X<sub>j<\/sub><\/em>, or a confounding arc between <em>L<sub>i<\/sub><\/em> and  <em>X<sub>j<\/sub><\/em> with <em>i<\/em> &lt;= <em>j<\/em>,  should not render the causal effect non-identifiable.  For example,  even if a confounding arc exists between <em>X<\/em><sub>2<\/sub>  and <em>X<\/em><sub>3<\/sub> (but no other confounding arcs  exist in the model), the causal effect on <em>Y<\/em> of setting  <em>X<\/em><sub>2<\/sub>=<em>x<\/em><sub>2<\/sub> and  <em>X<\/em><sub>3<\/sub>=<em>x<\/em><sub>3<\/sub>  should be the same as the distribution on <em>Y<\/em> if we observe <em>x<\/em><sub>2<\/sub> and <em>x<\/em><sub>3<\/sub>. <\/font><\/p>\n<p><font>It is also not necessary that the DAG be complete. <\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>From a previous correspondence with Eliezer S. Yudkowsky, Research Fellow, Singularity Institute for Artificial Intelligence, Santa Clara, CA The following paragraph appears on p. 103, shortly after eq. 3.63 in my copy of Causality: &quot;To place this result in the context of our analysis in this chapter, we note that the class of semi-Markovian models [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,15],"tags":[],"class_list":["post-29","post","type-post","status-publish","format-standard","hentry","category-book-j-pearl","category-g-estimation"],"_links":{"self":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/29","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=29"}],"version-history":[{"count":0,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/29\/revisions"}],"wp:attachment":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=29"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=29"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=29"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}