Inference on Discretely Observed Linear Birth-Death-Immigration Processes

• Activity Number: 427
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Charles R. Doss*+ and Vladimir Minin and Ian Holmes and Marc Suchard
• Companies: University of Washington and University of Washington and University of California, Berkeley and University of California, Los Angeles
• Keywords: Linear Birth-Death Process ; EM Algorithm ; Gibbs Sampler ; generating function ; data augmentation ; myobacterium tuberculosis

Abstract

We are interested in estimating parameters of linear birth-death-immigration (BDI) processes, observed discretely at unevenly spaced time points. Viewing this task as a missing data problem, we develop novel implementations of the expectation-maximization (EM) and Bayesian data augmentation algorithms. When the rate of immigration is constrained, we reduce the E-step of the EM algorithm as well as calculation of the Fisher information to one dimensional integration. To tackle the non-constrained immigration rate, we modify a direct sampler for finite state Markov chains; we use this for sampling in a Monte Carlo EM algorithm as well as in a Gibbs sampler in which we augment the BDI model parameters with missing continuous time trajectories. We test our algorithms on simulated data and then estimate birth and death rates of a transposable element in Myobacterium tuberculosis.