I am a fifth-year Ph.D. student in Statistics at Harvard University, supervised by Pierre Jacob. My research interests include agent-based models and Monte Carlo methods.
My Chinese name is written as 鞠念桥 and you can also call me Phyllis. You can contact me at nju AT g DOT harvard DOT edu.
I maintain a blog at phylliswithdata.com.
PhD in Statistics, 2021 (expected)
Harvard University
BA in Mathematics, 2016
Wellesley College
We consider a vector of $N$ independent binary variables, each with a different probability of success. The distribution of the vector conditional on its sum is known as the conditional Bernoulli distribution. Assuming that $N$ goes to infinity and that the sum is proportional to N, exact sampling costs order $N^2$, while a simple Markov chain Monte Carlo algorithm using ‘swaps’ has constant cost per iteration. We provide conditions under which this Markov chain converges in order $N\log N$ iterations. Our proof relies on couplings and an auxiliary Markov chain defined on a partition of the space into favorable and unfavorable pairs.