3:30pm to 4:45pm |
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The Foundations of Statistics: A Modern Perspective
(Seminar/Conference)
Professor Larry Wasserman (Departments of Statistics and Machine Learning at Carnegie Mellon) will deliever the inaugural "I.J. Good Lecture"*
ABSTRACT: In the past, statisticians interested in the foundations of Statistics were mainly concerned with the debate on Bayesian versus non Bayesian approaches. Most discussions focused on models with one or two parameters. Our intuition about inference was heavily guided by these simple, low dimensional models. Now, we routinely deal with very complex, high-dimensional models. Statistical theory and methodology has outstripped our understanding of foundations because we tend to cling to our low-dimension intuition.
I'll discuss some examples of high-dimensional inference including "sparse additive nonparametric regression", "stable density clustering", "semiparametric
undirected graphs" and "minimax estimation of manifolds". One foundational lesson we learn from these examples is that conditional methods and Bayesian methods can fail terribly in high dimensions. Also, we should give up any pretense of "estimating the truth" and instead focus on making accurate predictions and finding sparse, stable structure.
*Part of the Virginia Tech Distinguished Adjunct Lecture Series in Philosophy More information...
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