Estimation of Age of a Galton Watson Process

• Activity Number: 508
• Type: Contributed
• Date/Time: Thursday, August 2, 2007 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Satrajit Roychoudhury*+ and Pranab K. Sen and Manish C. Bhattacharjee
• Companies: Schering Plough Research Institute and The University of North Carolina at Chapel Hill and New Jersey Institute of Technology
• Keywords: Braching Process ; Galton Watson Process ; EM Algorithm ; Age

Abstract

There are several situations where we might want to estimate the age of a Markov process. For example, we may be interested in estimating the length of time a species has been in existence in its present form, without having much historic information such as fossils for carbon dating. Also, in the genetic context, the usual problem is to find the age of an allele, given its current frequency, which means, estimating the time point when a mutation took place. For a discrete time branching process or Galton Watson Process, its age is the generation that corresponds to the earliest observed value. Three different methods of estimation of `age' are discussed along with examples. An EM algorithm is developed to estimate the parameters of offspring distribution. All the estimators have been developed in the nonparametric setup, assuming no parametric form of the offspring distribution.