Visually Identifying Potential Domains for Change Points in Generalized Bernoulli Processes: an Application to DNA Segmental Analysis

A Bernoulli process is a discrete-time stochastic process consisting of a finite or infinite sequence of i.i.d. random variables Y1, Y2, Y3, · · ·, and Y1 has Bernoulli distribution with mean p. Following the generalization of binomial distribution given by Drezner and Farnum (1993), we name a process {Yt} a generalized Bernoulli process if, for all t > 0, Yt has Bernoulli distribution with mean pt > 0, where Y1, Y2, Y3, · · · are not necessarily independent and pt are not necessarily all the same. In this paper, without further notice, we are only interested a special scenario of generalized Bernoulli processes, where all Yt are mutually independent. A Bernoulli process is a special generalized Bernoulli process where all pt = p.