Ancestral Inference for Branching Process in Random Environments

Oregon Convention Center 

Ancestral inference for Branching processes in random environments (BPRE) is concerned with the inference regarding the parameters of the ancestor distribution generating the process. In this presentation, we describe a new generalized method of moments methodology for inference using replicated BPRE data. Even though the evolution of the process strongly depends on the offspring means of various generations, we establish that the joint limiting distribution of the ancestor and the offspring estimators mean, under appropriate centering and scaling, decouple and converge to independent normal random variables when the ratio of the number of generations to the logarithm of the number of replicates converge to zero. We also provide estimators for the limiting variance and illustrate our results using numerical experiments and data from Polymerase Chain Reaction (PCR) experiments.

BPRE

Ancestral Inference

Joint CLT

PCR 

IMS