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I am working on genomic selection and I am comparing the performance of two models, one of them is a likelihood method (GBlup) and the other is a Bayesian meyhod (Bayesian Ridge Regression). I am looking at the variance component and they are not exactly equal. So I wounder if it estimates should be equal. Anyone that have some idea?

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  • $\begingroup$ Why should completely different methods give the same answer? For BLUP see for example this link. For Bayesian ridge regression stats.stackexchange.com/a/328345/99274. $\endgroup$
    – Carl
    Apr 6 '20 at 14:19
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    $\begingroup$ Hi, thank you for your comment. I got confused with the next statement: The β in BRR will be equal to the RR estimate with, λ= σε^2/σβ^2 , therefore it is also the BLUP of β given y. RR and BRR both perform an extent of shrinkage that is homogenous across markers (de los Campos et al. 2013) According to this, I interpreted It can be similar... $\endgroup$
    – marb_021
    Apr 6 '20 at 16:15
  • $\begingroup$ It would help if you linked to the work in which that statement is made. Ridge regression reduces variance by injecting bias so that if all that is being done by comparison is ML that will not be the case. $\endgroup$
    – Carl
    Apr 6 '20 at 17:42
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GBLUP is mathematically equivalent to RR-BLUP when the genetic covariance matrix $G$ is calculated as $G=XX^T$from the data matrix $X$ (where each column of $X_{ij}$ is the value of the $j$th property (e.g. SNP) of the $i$th individual.

Also, the estimates of Bayesian Ridge regression are equivalent to the estimates of ridge regression. This review has it all in section 2.2.: Jacquin et al., 2016.

I would suspect from this that the estimates could be equal, but I'm not sure...

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