### Talk by Jean-Pierre Dion (Université du Québec à Montréal, visiting USC)

Date and Time: Thursday, November 10, 2005, 10:00 AM in AP&M 6218.

Title: The efficiency of polymerase chain reactions measured
through age-dependent branching processes

Abstract: Polymerase Chain Reaction (PCR) is an in vitro technique
aimed at creating multiple copies of a given nucleotide sequence.
In principle, after each PCR cycle there should be a duplication of
the molecules so that after n cycles there should be N(0) 2^n
molecules, where N(0) is the number of initial molecules.
In practice there is a probability p of duplication at each cycle,
with p less than one. This value measures the efficiency of the
duplication process and it may be constant through the cycles or
varying in a random or deterministic way. We use the age dependent
branching process model to estimate the efficiency and show the
consistency and asymptotic Normality of the quasi-likelihood
estimator. We also present a simulation study done by
Claude Gravel (M.Sc. thesis, UQAM, 2005) on the small sample
properties of the estimator. These results are useful for the
related important problem of estimating the initial number of
molecules (the concentration) if unknown.