Is there any consistency guarantee between CS and joint PIP

[garyzhubc]

It says in the paper: "Arguably, this is exactly the kind of posterior summary that we would like to obtain from Markov chain Monte Carlo based or stochastic search BVSR methods, but doing so would require non-trivial post-processing of their output. In contrast, our method provides this posterior summary directly, and with little extra computational effort."

Is there any consistency guarantee between CS and joint PIP? That is, if I create an algorithm that enumerate and search all subsets whose sum of joint PIP is greater or equal to some coverage, will it lead me to the same CS generated by SusieR?

[pcarbo]

The SuSiE variational approximation assumes independence of the single effects. This assumption can be violated of course, so there is no consistency guarantee.

Perhaps exploring this more could lead to an interesting research direction.

[garyzhubc]

I tried to compute joint PIP with marginal PIPs but I realized some variants has PIP zero.

For instance, the Joint PIP that the variant is in the middle third:

prod(1-res_$pip[1:34])*(1-prod(1-res_$pip[35:68]))*prod(1-res_$pip[69:101])

gives zero. So would it be fair to claim that the credible sets SusieR chooses are of very small probabilities?

[garyzhubc]

I tried to compute joint PIP with marginal PIPs but I realized some variants has PIP zero.

For instance, the Joint PIP that the variant is in the middle third:

prod(1-res_$pip[1:34])*(1-prod(1-res_$pip[35:68]))*prod(1-res_$pip[69:101])

gives zero. So would it be fair to claim that the credible sets SusieR chooses are of very small probabilities?

Also wondering if this calculation is correct. Shall I be summing or multiplying PIPs to get joint PIP?