192
University of New Mexico
Abstract:There are many practical issues such as
logistics support, duration of study, and potential high
drop-out rate in clinical trial study. In particular, when
there are 4 or more treatments under consideration.
To overcome these issues, researchers use incomplete
block crossover design when patients receive only a
subset of treatments under comparison.
In this article, we propose a Bayesian approach to test
treatment effects for binary data in a 4X4 Latin-square.
We use several approaches such as dta augmentation,
scaled mixture of normals, and parameter expansion
to improve efficiency. The approach is illustrated with
a simulation study and a real data example.
Asymptotic Inference Theory of the Hawkes Process with Time-Varying Baseline Intensity and a
General Excitation Kernel
Jeffrey Kwan
University of New South Wales
Abstract:The Hawkes process is a popular point
process model for event sequences that exhibit a temporal clustering behavior. A natural way of measuring
the rate of occurrence of points of a point process is
via its intensity function. The intensity of a Hawkes
process consists of two components, the baseline intensity and the excitation kernel. The classical
Hawkes process assumes a constant baseline intensity
and an exponential excitation kernel. This results in an
intensity process that is Markovian. However, the
assumptions imposed by the classical Hawkes process
can be restrictive and unrealistic for certain modelling
purposes. By allowing the baseline intensity to vary
with time, and the excitation kernel to be
non-exponential, such a setup expands the modelling
capacity of the classical Hawkes process. However,
asymptotic inference under this setup is substantially
more difficult since the resulting intensity process is
non-Markovian, thus rending standard techniques for
asymptotic inference of Markov processes futile. To
overcome this challenge, we devised an approximation procedure to show the intensity process is asymptotically ergodic. This allows for the identification
of an ergodic limit to the likelihood function. Consequently, by taking a parametric approach and under
minimal regularity conditions, asymptotic results for
likelihood based statistical inference, for example,
consistency and asymptotic normality of the maximum likelihood estimator, can be achieved.
Joint work with Feng Chen, William Dunsmuir.
Contributed Session CS043: Recent Advances in
Differentially Private and Complex Data Model
Causal Inference in Randomized Experiments for
Dyadic Data
Yilin Li
Peking University
Abstract: Estimating the total average treatment
effect on a network could be considerably biased due
to spillover effects in the presence of unknown network interference. We consider novel dyadic outcomes in the presence of interference. Such outcomes
are common in many social network sources, such as
forwarding a message or sharing a link. We first introduce the setting of network interference with dyadic outcomes, which is of particular interest in online
experimentation. Then we manifest that the unbiased
estimator for the total average treatment effect based
on the conventional outcomes does not exist under
heterogeneous treatment effects. We provide subsequently unbiased estimators based on dyadic outcomes for randomized experiments. We show the
possible variance bounds of our proposed estimators
and provide a variance estimator to quantify the uncertainty. We illustrate the above phenomenon with a
variety of numerical experiments. We utilize our
method and discuss further applications scenarios.
Joint work with Lu Deng, Yong Wang, Wang Miao.
Optimal Locally Private Nonparametric Classification with Public Data
Yuheng Ma
Renmin University of China
Abstract:In this work, we investigate the problem of
public data-assisted non-interactive LDP (Local Differential Privacy) learning with a focus on
non-parametric classification. Under the posterior drift
assumption, we for the first time derive the mini-max