Use of Runs Statistics for Pattern Recognition in Genomic DNA Sequences

Abstract

In this article, the use of the finite Markov chain imbedding (FMCI) technique to study patterns in DNA under a hidden Markov model (HMM) is introduced. With a vision of studying multiple runs-related statistics simultaneously under an HMM through the FMCI technique, this work establishes an investigation of a bivariate runs statistic under a binary HMM for DNA pattern recognition. An FMCI-based recursive algorithm is derived and implemented for the determination of the exact distribution of this bivariate runs statistic under an independent identically distributed (IID) framework, a Markov chain (MC) framework, and a binary HMM framework. With this algorithm, we have studied the distributions of the bivariate runs statistic under different binary HMM parameter sets; probabilistic profiles of runs are created and shown to be useful for trapping HMM maximum likelihood estimates (MLEs). This MLE-trapping scheme offers good initial estimates to jump-start the expectation-maximization (EM) algorithm in HMM parameter estimation and helps prevent the EM estimates from landing on a local maximum or a saddle point. Applications of the bivariate runs statistic and the probabilistic profiles in conjunction with binary HMMs for pattern recognition in genomic DNA sequences are illustrated via case studies on DNA bendability signals using human DNA data.

Computation of exact probabilities associated with overlapping pattern occurrences

“…Computation of distributions of statistics associated with overlapping pattern occurrences through generating functions, correlation functions, the Goulden–Jackson cluster method, recursive computation, and Markov chain‐based methodology have been presented in this article. While theory on computing distributions of patterns statistics in Markovian sequences is well‐established, in recent years, researchers have extended the work to more complicated models, for example, data generated by a hidden Markov model (HMM) (Cheung, ; Régnier, Furletova, Yakovlev, & Roytberg, ), and pattern distributions associated with occurrences in hidden states of HMMs (Aston & Martin, ) and conditional random fields (Martin & Aston, ).…”

Sakli Markov Modeli̇ Kullanilarak Seçmen Terci̇hleri̇ni̇ Etki̇leyen Faktörleri̇n Beli̇rlenmesi̇

“…SM Modeli, zaman serisi olaylarını analiz etmek ve tahmin etmek için yaygın olarak kullanılan araçlardır. Bu metot, DNA dizi analizi (Cheung, 2004), konuşma sinyali tanıma (Xie vd, 2004), EKG analizi (Coast vd, 1990), trafik mühendisliği (Dainotti A.vd, 2008), metroloji (Zucchini W., Guttorp P,1991: Robertson vd, 2004, biyoloji (Leroux B. G. ve Puterman M. L., 1992), finans/ekonometri (MacDonald ve Zucchini,1997;Hamilton,1994;Kim ve Nelson,1999), yazılım güvenilirliği (Ruggeri ve Soyer, 2012;Landon vd, 2013), deprem problemleri (Ebel vd., 2007;Granat ve Donnellan, 2002) dâhil olmak üzere çeşitli zaman serilerini analiz etmek için başarıyla kullanılmıştır. Bu çalışmada da SM modeli gelecek seçimlerde seçmenlerin siyasi parti tercihlerini etkileyen faktörlerin belirlenmesine yönelik kullanılmıştır.…”

Aggregate Claim Estimation Using Bivariate Hidden Markov Model

“…An optimal way is to assume that the parameter process must satisfy the Markov property leading to HMM due to its nature. HMMs have been applied in various fields, namely speech recognition (Rabiner and Juang, 1993), molecular biology (Krogh et al, 1994), analysis of DNA sequence (Cheung, 2004), and stock market forecasting (Hassan and Nath, 2005). The main reason for selecting an HMM for modeling the claim dependence is that unobservable background factors triggering the claim-causing events can be characterized and captured by a hidden parameter process.…”