Thu, October 11, 2018
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3:00pm [3:00pm] Prof. Alexander Volfovsky Department of Statistical Sciences Duke University
Speaker: Prof. Alexander Volfovsky Department of Statistical Sciences Duke University Date and Time: Thursday, 11/10/2018, 3:00 pm -- 4:00 pm Venue: Ramanujan Hall Title: Design of experiments for networks with interference Abstract: Randomized experiments have long been considered to be a gold standard for causal inference. The classical analysis of randomized experiments was developed under simplifying assumptions such as homogeneous treatment effects and no treatment interference leading to theoretical guarantees about the estimators of causal effects. In modern settings where experiments are commonly run on online networks (such as Facebook) or when studying naturally networked phenomena (such as vaccine efficacy) standard randomization schemes do not exhibit the same theoretical properties. To address these issues we develop a randomization scheme that is able to take into account violations of the no interference and no homophily assumptions. Under this scheme, we demonstrate the existence of unbiased estimators with bounded variance. We also provide a simplified and much more computationally tractable randomized design which leads to asymptotically consistent estimators of direct treatment effects under both dense and sparse network regimes.

4:00pm [4:00pm] Vivek Tewary
Title: Bloch Wave Homogenization of Almost Periodic Operators Speaker: Vivek Tewary, PhD student, Department of Mathematics, IIT Bombay, Time: 4 p.m.- 5p.m., 11-10-18, Thursday. Venue: Room 215, Department of Mathematics Abstract: Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost periodic operators. In particular, the notion of Bloch eigenvalues and eigenvectors does not exist for almost periodic operators. However, we are able to recover the homogenization result in this case, by employing a sequence of periodic approximations to the almost periodic operator.