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AMS Weekly Seminar | Alden Green

September 25 @ 1:30 pm - 2:30 pm

Location: Krieger 205

When: September 25th at 1:30 p.m.

Title: Selective peak inference for signal localization in multiple testing

Abstract: Many applications of high-dimensional multiple hypothesis testing in domains such as neuroimaging and genomics feature a spatial or temporal component, with each test corresponding to a location or time point. An important part of such problems is signal localization: that is, alternative hypotheses are often clustered together into contiguous regions, and the underlying goal is to conduct inference on these “active’’ regions. Traditional pointwise tests are inappropriate for this task. An alternate approach is peak inference, in which active regions are summarized by their local maxima (“peaks’’) and one conducts statistical inference for true peaks using peaks observed in the data.

In this talk I propose a new two-stage method for peak inference. In the first stage, a subset of the observed peaks are selected by thresholding, with the threshold chosen to control the probability of selection under the null hypothesis that no signal is present. The second stage uses those peaks that remain to construct confidence regions for the location and height of any nearby true peak. I will discuss theoretical guarantees showing that as the signal strength and threshold grow our method for peak inference after selection has asymptotically nominal coverage for both location and height. Both method and theory are derived using the theory of Gaussian Random Fields (RFT), in particular the Kac-Rice formula for the expected number of critical points of a random smooth function.
I will also discuss a randomized version of our method that results in narrower intervals (for the height) and more accurate coverage (for the location).
This is based on joint work with Jonathan Taylor.

Zoom link: https://wse.zoom.us/j/93600407710?pwd=JBL8VsObRxX6MkhdjAUxCadqJDoZrZ.1

Details

Date:
September 25
Time:
1:30 pm - 2:30 pm
Event Category:

Venue

Krieger 205
3400 North Charles Street
Baltimore, Maryland 21218 + Google Map