Fractional poisson process: Long-range dependence in DNA sequences

Article type: Research Article

Authors: Linhares, Raquel Romes

Affiliations: Faculty of Mathematics, Federal University of Uberlândia, Minas Gerais, Brazil | E-mail: [email protected]

Correspondence: [*] Corresponding author: Faculty of Mathematics, Federal University of Uberlândia, Minas Gerais, Brazil. E-mail: [email protected].

Abstract: Modeling DNA sequences with stochastic models and developing statistical methods to analyze the multiple projects of DNA sequencing are challenging questions for statisticians and biologists. Some of the most manifestations are the study of long-range dependence in DNA sequences that transform the DNA sequence into a numerical time series to study the long-range dependence in a DNA sequence. It is still discussed in the works if the type of transformation can alter the conclusion of long-range dependence on the DNA sequence. Here we model the DNA sequence considering the Fractional Poisson Process, propose a method based on moments for estimating the parameters of the Fractional Poisson Process in the DNA sequence, and analyze the long-range dependence in various DNA sequences by the detrended fluctuation analysis method.

Keywords: Long-range dependence, fractional poisson process, DNA sequence, DFA

DOI: 10.3233/MAS-210375

Journal: Model Assisted Statistics and Applications, vol. 18, no. 1, pp. 33-43, 2023