The seminar will be online. |
Zoom link: https://tudelft.zoom.us/j/97814167086?pwd=QWdaTkUzKzBUQmhMNTVDaWJKeGg5QT09
Meeting ID: 978 1416 7086
Titles and abstracts
Imprecise probability and valid statistical inference
Statistics aims to provide reliable or valid data-driven uncertainty quantification about unknowns. The two dominant schools of thought on this are frequentist and Bayesian, but the dichotomy creates confusion and masks opportunities for new developments. My perspective is that these are opposite ends of a spectrum indexed by the degree of precision in one's prior specification: Bayesian is completely precise, frequentist is vacuous or completely imprecise. To formalize this, I will make use of what I call an inferential model (IM), a generalization of Bayes, fiducial, etc., that allows for imprecision. First, I'll show that even a basic notion of validity cannot be achieved with a precise IM, so frequentist inference must correspond to an imprecise IM. Second, I'll show that a simple kind of imprecise IM, called a "possibility measure", can achieve validity and, moreover, that all frequentist procedures can be characterized by a possibility measure. Finally, I'll discuss practical implications of this characterization, open problems, and new directions.
This talk is largely based on work presented in the paper available here: https://researchers.one/articles/21.01.00002
Free Lunches and Approximate Markov chain Monte Carlo
It is widely known that the performance of MCMC algorithms can degrade
quite quickly when targeting computationally expensive posterior
distributions, including the posteriors associated with any large
dataset. This has motivated the search for MCMC variants that scale well
for large datasets. One general approach, taken by several research
groups, has been to look at only a subsample of the data at every step.
In this talk, we'll discuss some basic "no-free-lunch" results that
sometimes provide limits on the performance of many such algorithms.
We'll then apply these generic results to realistic statistical problems
and proposed algorithms. Finally, I'll discuss some of the many examples
that can avoid our generic results; some of these seem to provide a free
(or at least cheap) lunch, while others are (to my knowledge) open
(Based primarily on work with James Johndrow and Natesh Pillai, as well
as Patrick Conrad, Andrew Davis, Youssef Marzouk, Tanya Schmah, Pengfei
Wang and Aimeric Zoungrana.)
The Van Dantzig seminar is a nationwide series of lectures in statistics,
which features renowned international and local speakers, from the full width of
the statistical sciences. The name honours David van Dantzig (1900-1959), who
was the first modern statistician in the Netherlands, and professor in the "Theory
of Collective Phenomena" (i.e. statistics) in Amsterdam. The seminar will convene
4 to 6 times a year at varying locations, and is supported financially by among others
the STAR cluster and the Section Mathematical Statistics of the VVS-OR.