Van Dantzig Seminar

nationwide series of lectures in statistics

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Van Dantzig Seminar: 8 October 2015

Programme: (click names or scroll down for titles and abstracts)

 13:30 - 13:35 Opening 13:35 - 14:35 Martin Wainwright (UC Berkeley) 14:35 - 14:55 Break 14:55 - 15:55 Wolfgang Polonik (UC Davies) 15:55 - 16:25 Giulia Cereda (Leiden University and University of Lausanne) 16:30 - 17:30 Reception
 Location: Leiden University, Snellius Building, Room 408 (Directions)

Titles and abstracts

• Martin Wainwright

Statistical Estimation with Privacy Constraints: How to characterize the trade-offs?

With data being collected at unprecedented scales, the interaction between privacy and statistics has become increasingly important. There are obvious tensions between the requirement of preserving individual privacy versus that of performing statistical estimation with aggregated data. How does one formalize and characterize the associated trade-offs? Working under local differential privacy—a model in which aspects of the data remain private even from the statistician—we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. Our results reveal a surprising phenomenon: privacy constraints can lead to very different rates for canonical problems like estimating location parameters, as well as non-parametric density estimation.

Based on joint work with John Duchi, Stanford and Michael Jordan, UC Berkeley

• Wolfgang Polonik

Nonparametric Inference for Geometric Objects

Inference for geometric objects such as level sets, ridge lines and integral curves of densities or regression functions received quite some interest recently. In this talk we will review some of this recent work and present some new results about the asymptotic distribution of a plug-in estimator for ridge lines (or filaments). The derivation of the latter requires a result about the extreme value behavior of certain non-stationary Gaussian random fields indexed by growing manifolds, which is discussed also. This extreme value result can be considered as a generalization of some classical work by Bickel and Rosenblatt (1973) and work by Piterbarg and Stamatovich (2001).

This is joint work with Wanli Qiao, University of California, Davis

• Giulia Cereda

Non parametric Bayesian approach to LR assessment in case of rare type match

The evaluation of a match between the DNA profile of a stain found on a crime scene and that of a suspect (previously identified) involves the use of the unknown parameter $$\mathbf{p}=(p_1, p_2, ...)$$, (the ordered vector which represents the frequencies of the different DNA profiles in the population of potential donors) and the names of the different DNA types. We propose a Bayesian non parametric method which considers $$P$$ as a random variable distributed according to the two-parameter Poisson Dirichlet distribution, and discards the information about the names of the different DNA types. The ultimate goal of this model is to evaluate DNA matches in the rare type case, that is the situation in which the suspect's profile, matching the crime stain profile, is not in the database of reference.

http://arxiv.org/abs/1506.08444