{"id":20232,"date":"2012-07-13T10:07:54","date_gmt":"2012-07-13T16:07:54","guid":{"rendered":"http:\/\/rankexploits.com\/musings\/?p=20232"},"modified":"2012-07-13T14:53:20","modified_gmt":"2012-07-13T20:53:20","slug":"effect-of-covariance-screening-on-method-i","status":"publish","type":"post","link":"https:\/\/rankexploits.com\/musings\/2012\/effect-of-covariance-screening-on-method-i\/","title":{"rendered":"Effect of covariance & Screening on Method I."},"content":{"rendered":"

Bo emailed me with questions and comments on my previous post<\/a>. He was curious what happens to some of my graphs if I remove the covariance between the target temperature and the proxy response parameter $latex \\lambda_{i} $. I thought you guys might be too. So I created these graphs. Each compares the screened by correlation during the calibration period and unscreened results if I screening using local<\/I> temperatures. Each case is done at a different magntidue of correlation between $latex \\lambda_{i} $ and $latex T_{i} $. (The convention followed in the legend is negative is based on the trend<\/i> during the calibration period which is a sign error. But I started that way and haven’t fixed the sign error in the legend yet.) I’m showing screening with local values because that a lighter<\/I> level of screening (and so better!) <\/p>\n

Below, I’ve compared the synthetic results with $latex cov [ \\lambda_{i} $ and $latex mean[T_{i}] = 0. ] $.<\/p>\n

\"\" <\/a><\/p>\n

Above you can see that the screening picked out 4123 out of 5000 proxies (false rejecting 877 as ‘bad’). The consequence is the screened results have a slight bias during the reconstruction period; this bias results in the aqua trace being consistently higher than the black line representing the target. In contrast, the red line is unbiased. <\/p>\n

Positive covariance between “T and gamma”:<\/strong>
\nI repeated the exact same runs, but this time set the synthetic runs to make proxies were “warm” during the pre-calibration periods more reponsive to temperature variations and those that were “cold” during the historic period less so.
\n\"\"<\/a>
\n several things:<\/p>\n

    \n
  1. Looking at the red (unscreened) trace, we can see method I is too warm during the reconstruction period. But also, the reconstruction in method I does not follow the target well during the calibration period. What this means is that when the bias exists, someone is likely to notice the issue. (Inspecting the algebra shows why this happens.) This effect could be called the the fundamental bias in method I. It’s in the math. This effect is peculiar to method I (and is a reason one might wish to avoid method I.)<\/li>\n
  2. Looking at the aqua trace wee see that method I becomes even warmer<\/em> when the proxies are screened. This extra warming over an above the amount seen in the red line happens because screening picks out proxies that response better to the local temperature during the calibration period. Absent covariance local temperature and the proxy, this results in a warming bias seen above. Since the responsiveness is better at higher temperatures, the 4123 proxies that were retained were on average warmer during the reconstruction period than the original 5000 proxies. This results in a warm bias. And on top of that, we have the warming bias introduced by the existence of the correlation which we see in the red trace. So we have three separate effects all resulting in warming bias when correlation between the average temperature at a proxy during the reconstruction period and it’s responsiveness to temperature is positive.\n <\/li>\n<\/ol>\n

    Note that when correlation exists and<\/I> and we screen we will find that the underlying temperature at the selected proxies (i.e. the the 4123 proxies ones retained here) is biased relative to the full 5000 samples. This will happen with any method and is not unique to method A. So, when this correlation is not zero, some bias can be introduced into many methods even if it’s not introduced absent screening. (Some methods may, however, be immune to this. We would need to examine each one individually.)<\/p>\n

    Bo also wants to see how things look if I use fewer proxies– something closer to the number of proxies one might obtain for a real reconstruction. I’ll be posting some of those on Monday. I need to figure out how I want to show that because with fewer proxies, I think it’s best to show several realizations for each method. <\/p>\n

    I want to look add method IV for rescaling results– it will match the final step in Mann08. I haven’t yet figured out how I do RegEm with proxies. But I’ll think about that. I do want to see how each method works on toy problems. \ud83d\ude42<\/p>\n","protected":false},"excerpt":{"rendered":"

    Bo emailed me with questions and comments on my previous post. He was curious what happens to some of my graphs if I remove the covariance between the target temperature and the proxy response parameter $latex \\lambda_{i} $. I thought you guys might be too. So I created these graphs. Each compares the screened by … Continue reading Effect of covariance & Screening on Method I.<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[420],"class_list":["post-20232","post","type-post","status-publish","format-standard","hentry","category-statistics","tag-screening"],"_links":{"self":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts\/20232","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/comments?post=20232"}],"version-history":[{"count":0,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts\/20232\/revisions"}],"wp:attachment":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/media?parent=20232"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/categories?post=20232"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/tags?post=20232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}