Graduate Students Seminar

Speaker 1: Ji Li

Title

Longitudinal Data Analysis Using Marginal Models and Random Effects Models

Abstract

Longitudinal data can be collected either prospectively, following subjects forward in time, or retrospectively, by extracting multiple measurements on each person from historical records. To analyze the Longitudinal data, first we can do exploratory data analysis to visualize patterns in data.  Then we introduce regression methods that characterize the marginal expectation of a discrete or continuous response, Y, as a function of explanatory variables. Finally, we describe the generalized linear mixed model. It is an extension of a linear regression model to model longitudinal (correlated) data. It contains fixed effects and random effects where random effects are subject-specific and are used to model between-subject variation and the correlation induced by this variation.

Speaker 2: Mingkai Yu

Title

Sampling of discretely partial observed stochastic reaction networks

Abstract

Reaction networks are an important modeling tool in areas such as epidemiology, system biology and population ecology. They can be modeled by a discrete state continuous-time Markov process, where the state vector represents the number of each species at time t. We consider the task of generating samples from a Markov process between two time points, at which the exact observation of some of the state is known. We present two Monte Carlo simulation algorithms addressing this problem. A straightforward naive method simply discards the trajectories that don't match with the observation, but is typically very inefficient. We propose a weighted sampling algorithm that ensures all sample paths landing at the observed state and assigns associated importance weights arising from the Girsanov transformation of probability measures. Lastly, we show simulation results of both methods applying to an example.