##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability and Statistics

## Jean-Pierre Dion

#### Université du Québec à Montréal

## 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.

Host: Jason Schweinsberg

### November 10, 2005

### 9:00 AM

### AP&M 6218

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