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BEGIN:VEVENT

CATEGORIES:Natural Sciences
CATEGORIES:Utilities
CATEGORIES:Main
CONTACT;X-BEDEWORK-UID=00f1fcdb-0f068baf-010f-068baf83-00000004:None
CREATED:20250108T202036Z
DESCRIPTION:We investigate inference for a single coordinate in high-dimen
 sional linear regression\, focusing on settings where there is a single p
 arameter of interest (such as a treatment effect) in the presence of nume
 rous potential confounding covariates. A common Bayesian procedure in suc
 h scenarios is to model the nuisance covariates using a model selection p
 rior\, which encourages sparsity in the regression coefficients. \n\nThis
  work characterizes the behavior of the model selection posterior distrib
 ution for the coordinate of interest as sample size grows. Under certain 
 conditions\, we establish that the posterior marginal distribution achiev
 es optimal inferential properties through a Bernstein-von Mises theorem: 
 it converges to a normal distribution centered at an efficient oracle est
 imator with optimal variance. Strikingly\, such performance is attainable
  under conditions where other priors or frequentist procedures such as th
 e LASSO require debiasing. \n\nHowever\, we also identify settings where 
 the posterior marginal exhibits problematic limiting behavior\; convergin
 g to a multimodal mixture with components that contain substantial bias a
 nd/or suboptimal variance\, resulting in poor coverage. We propose adjust
 ments to the prior specification that provably restore desirable asymptot
 ic properties whenever such issues arise.
DURATION:PT1H
DTSTAMP:20250108T211042Z
DTSTART;TZID=America/New_York:20250117T153000
LAST-MODIFIED:20250108T211042Z
LOCATION;X-BEDEWORK-UID=18832edc-1b27e154-011b-28365daf-0000006c:Old Chemi
 stry 116
STATUS:CONFIRMED
SUMMARY:Bayesian Linear Regression with a Sparse Prior: Inference for a Si
 ngle Coordinate
UID:CAL-8a000483-92c3adf6-0194-47937fe4-00002ad6demobedework@mysite.edu
X-BEDEWORK-ALIAS;X-BEDEWORK-PARAM-DISPLAYNAME=Main:/user/public-user/Utili
 ties/Main
X-BEDEWORK-ALIAS;X-BEDEWORK-PARAM-DISPLAYNAME=Natural Sciences:/user/publi
 c-user/Topics/Natural Sciences
X-BEDEWORK-SPEAKER:Lasse Vuursteen\, Postdoctoral Scholar\, University of 
 Pennsylvania\, Wharton School of Business
X-BEDEWORK-SUBMITTEDBY:tnscott for Statistical Science (agrp_StatisticalSc
 ience)
X-BEDEWORK-IMAGE-X1:0
X-BEDEWORK-IMAGE-Y1:-0.3333333333333144
X-BEDEWORK-IMAGE-X2:530
X-BEDEWORK-IMAGE-Y2:353
X-BEDEWORK-IMAGE-CROP-WIDTH:530
X-BEDEWORK-IMAGE-CROP-HEIGHT:353.3333333333333
X-BEDEWORK-IMAGE-ALT-TEXT:Lasse Vuursteen
X-BEDEWORK-IMAGE:/public/Images/Lasse-1.17_20250108091042PM.jpg
X-BEDEWORK-THUMB-IMAGE:/public/Images/Lasse-1.17_20250108091042PM-thumb.pn
 g
END:VEVENT
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