http://www.win-vector.com/blog/2009/10/google-adsense-channels-ids-and-the-cramer-rao-inequality/?utm_source=rss&utm_medium=rss&utm_campaign=google-adsense-channels-ids-and-the-cramer-rao-inequality The Applied Theorist's Point of View Thu, 15 Jul 2010 00:13:50 +0000 hourly 1 http://wordpress.org/?v=3.0.1 http://www.win-vector.com/blog/2009/10/google-adsense-channels-ids-and-the-cramer-rao-inequality/comment-page-1/#comment-1784 jmount Tue, 19 Jan 2010 01:35:51 +0000 http://www.win-vector.com/blog/?p=898#comment-1784 <a href="#comment-1780" rel="nofollow">@John </a> A very interesting point. I would caution that the likelihoods you would want to calculate (say in the section 3.2.1 example) in a Bayesian procedure would essentially be functions of the summary statistics that are not very tightly related to the parameters you are trying to estimate (due to the unfortunate censoring process of only being allowed a constant number nearly co-linear measurements). So I think you run into similar problems. As the number of (hidden) data items gets large I would expect the Bayesian estimate to get near the linear algebra estimate (which is itself having trouble). I emphasize that the unfortunate sum-ups were not part of the estimation procedure, but part of the externally imposed problem structure. @John
A very interesting point. I would caution that the likelihoods you would want to calculate (say in the section 3.2.1 example) in a Bayesian procedure would essentially be functions of the summary statistics that are not very tightly related to the parameters you are trying to estimate (due to the unfortunate censoring process of only being allowed a constant number nearly co-linear measurements). So I think you run into similar problems. As the number of (hidden) data items gets large I would expect the Bayesian estimate to get near the linear algebra estimate (which is itself having trouble). I emphasize that the unfortunate sum-ups were not part of the estimation procedure, but part of the externally imposed problem structure.

]]> http://www.win-vector.com/blog/2009/10/google-adsense-channels-ids-and-the-cramer-rao-inequality/comment-page-1/#comment-1780 John Mon, 18 Jan 2010 23:01:52 +0000 http://www.win-vector.com/blog/?p=898#comment-1780 This is exactly why you shouldn't be using unbiased estimation. Bayesian estimation avoids all these problems and is consistent with what your actually trying to do: maximize profit. This is exactly why you shouldn’t be using unbiased estimation. Bayesian estimation avoids all these problems and is consistent with what your actually trying to do: maximize profit.

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