Yuval Benjamini - Measuring bumps: Selection-corrected inference for detected regions in high-throughput data

13 months ago by
Yuval Benjamini Slides (PowerPoint)

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13 months ago by
Yuval Benjamini slides in pdf (click here)
13 months ago by
Paper related to this talk: http://www.biorxiv.org/content/early/2016/10/23/082321
13 months ago by
The definition of a bump is an unbroken run of values above the cutoff.  With a relatively long run that only marginally crosses the boundary, there might be a non-negligible probability of splitting one bump into two, or vica versa.  What is the impact of this on the operation of your procedure?
Good question. 
It will not break the method; we will report two regions.
The FDR might be hurt by correlated p-values, but it is usually robust to these issues in practice. 
It will hurt power and interpretability. 

The signal left for inference after conditioning away the "under the threshold" 
is independent from the size of the bump. 
But this also means that if the bump is long enough
(and correlation within subject is not too high), it will usually be considered "significant" with even only few of the points are somewhat above the threshold.

Note that the method will usually be run after smoothing the data, which might somewhat mitigate this problem (not sure if it solves completely).
Conceptually, you can allow skipping a single location, but that becomes a bit more complicated in the sampling.  
We are now thinking of inference in a multi resolution signal, but no ready ideas how to do selective inference in this context.
written 13 months ago by Yuval Benjamini 
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