Statistics
http://events.berkeley.edu/index.php/calendar/sn/stat.html
Upcoming EventsBLISS Seminar: Queues, Balls and Bins, and Association, Mar 19
http://events.berkeley.edu/index.php/calendar/sn/stat.html?event_ID=116306&date=2018-03-19
We consider a problem motivated by file retrieval in cloud computing systems where storage coding is used. In such problems, each file-retrieval job consists of multiple tasks (each corresponding to the retrieval of a coded chunk of a file), and the job is completed only when all of its tasks are completed. The goal is to compute the tail probability of the job completion time. However, this is a difficult problem whereas the problem of computing tail probabilities of task completion times is relatively easy. We will show that, by assuming that the task completion times are independent, one can compute an upper bound on the tail probability of the job completion time. The result is obtained by proving that the task completions times at the various servers in the cloud system are associated. The key step in the proof can be easily understood by considering a corresponding balls-and-bins problem as we will illustrate in the talk. Joint work with Weina Wang, Mor Harchol-Balter, Haotian Jiang, and Alan Scheller-Wolf.http://events.berkeley.edu/index.php/calendar/sn/stat.html?event_ID=116306&date=2018-03-19Formation of large-scale random structure by competitive erosion, Mar 21
http://events.berkeley.edu/index.php/calendar/sn/stat.html?event_ID=116303&date=2018-03-21
Competitive erosion models a random interface sustained in equilibrium by equal and opposite<br />
pressures on each side of the interface. Here we study the following one dimensional<br />
version. Begin with all sites of Z uncolored. A blue particle performs simple random walk<br />
from 0 until it reaches a nonzero red or uncolored site, and turns that site blue; then, a red<br />
particle performs simple random walk from 0 until it reaches a nonzero blue or uncolored<br />
site, and turns that site red. We prove that after n blue and n red particles alternately perform<br />
such walks, the total number of colored sites is of order n^1/4<br />
The resulting random color configuration has a certain fractal nature which after scaling by n^1/4 and taking a<br />
limit, has an explicit description in terms of alternating extrema of Brownian motions.<br />
This is joint work with Shirshendu Ganguly and Lionel Levine.http://events.berkeley.edu/index.php/calendar/sn/stat.html?event_ID=116303&date=2018-03-21A Unified Theory of Regression Adjustment for Design-based Inference, Mar 21
http://events.berkeley.edu/index.php/calendar/sn/stat.html?event_ID=116354&date=2018-03-21
Under the Neyman causal model, a well-known result is that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to experiments with more complex designs? This paper proposes a general framework for addressing this question and defines a class of generalized regression estimators that are applicable to experiments of any design. The class subsumes common estimators (e.g., OLS). Within that class, two novel estimators are proposed that are applicable to arbitrary designs and asymptotically optimal. The first is composed of three Horvitz-Thompson estimators. The second recursively applies the principle of generalized regression estimation to obtain regression-adjusted regression adjustment. A simulation study illustrates that the latter can be superior to alternatives in finite samples.http://events.berkeley.edu/index.php/calendar/sn/stat.html?event_ID=116354&date=2018-03-21