[ibayesclub.beta] Invitation: Bayes Club, 9th of April (Friday), 2-4 pm, zoom

[Szabo, B.T.]

Dear  Colleagues,

The next International Bayes Club (https://www.math.vu.nl/thebayesclub/) meeting will take place on the 9th of April (Friday) from 2 pm (CET). We have two speakers: Zacharie Naulet (Universite' Paris-Sud) and Emanuele Dolera (Pavia). Please find below the titles and the abstracts. After the talks we will open up our  virtual meeting place at gather.town so if you want to hang out and perhaps have a beer virtually with your colleagues then you are invited to join. The seminar will be on zoom:

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Topic: International Bayes club
Time: Apr 9, 2021 02:00 PM Amsterdam

Join Zoom Meeting
https://vu-live.zoom.us/j/93630288944?pwd=QnRMSUwwaFA1anYzWWZqdUN5WDZ5dz09

Meeting ID: 936 3028 8944
Passcode: 049612
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Link to the meeting place at gather town:

https://gather.town/app/4lK8Zj28Ys0WtutP/IBC
Password: bayesbayesbayes

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2 pm Speaker: Zacharie Naulet  (Universite' Paris-Sud)

Title: Minimax and Bayesian estimation of the unseen under tail-index regularity
Joint work with Stefano Favaro.

In this talk, I will discuss the famous problem of estimating the number of
unseen species in a population. This problem has a long history in statistics,
but has recently received a lot of attention after the breakthrough of Orlitsky
et al. who established impressive information-theoretical limits of
predictability of the unseen. For a suitable notion of loss, they proved that
minimax estimation of the unseen over all population distributions from a sample
of size $n$ is possible if and only if the population size is at most $o(n
\log(n))$. Their result is interesting in many ways, but perhaps deceptive for
statisticians, as the estimator they provide works only for large sample sizes.
This leaves open the problem of what can be done if we are willing to assume
regularity on the population distribution. On the Bayesian side, the literature
has largely investigated random partition models, giving many ways of estimating
the unseen. Most famous models, such as Poisson-Kingman partitions or Pitman-Yor
processes, generate populations that possess the property of having a finite
"tail-index" which entirely determine the asymptotic behaviour of the number of
species. Inspired by this long line of works, we do a minimax analysis of the
unseen problem over classes of population distributions having a finite
tail-index $\alpha \in (0,1)$. Albeit our analysis is mostly frequentist, the upper
bound is derived by constructing an estimator using BNP arguments and can be
easily extended to the classical Pitman-Yor estimates. Importantly, our
estimator can be efficiently computed, which I will support with some
simulations. The main challenge is on deriving the minimax lower bound. For this
matter, we propose a generic machinery for obtaining minimax lower bounds in
partition models which is of interest by itself as it can be used for many other
quantities. Interestingly, this machinery also relies on BNP arguments. In the
end, our main result is that estimating the tail-index and the unseen are
equivalent problems, and under suitable second-order assumptions on the
tail-index, minimax estimation of the unseen is possible all the way up to
population sizes that are as large as $o(\exp(c n^{\alpha})$ and impossible for larger
populations, in contrast with the $o(n \log(n))$ limit under no regularity
assumption.

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3 pm Speaker: Emanuele Dolera (Pavia)


Title: A new approach to Posterior Contraction Rates via Wasserstein dynamics


Abstract: please find it attached.
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