Geometric Process Modeling on Binary Data

• Activity Number: 161
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Pak Kei Ho*+
• Companies: University of Hong Kong
• Keywords: geometric process ; maximum likelihood ; Bayesian

Abstract

Much research has been done in the analysis of observations with trend. One of the widely used techniques is the nonhomogeneous Poisson (NHPP) process. If the successive interarrival times are monotone, the Cox-Lewis model and Weibull Process model are commonly used. We focus on the geometric process modeling, a more direct approach to model the data by a monotone process. A stochastic process {Xi, i=1,2,.} is a geometric process if there exists a>0 such that {Yi=a^(i-1)Xi} generates a renewal process. If the observations {Wi} are binary, we define Wi = I(Xi >1) = I(Yi > a^(i-1)) with the indicator function (the probit link function) I. Under the assumption that Yi follows Weibull distribution, we study the statistical inference for the geometric process on a binary dataset. Two approaches will be investigated: maximum likelihood and the second is Bayesian. Then, some suggestions and discussions will be made based on the simulation and real data analysis.