{"title":"Confidence intervals for Markov chain transition probabilities based on next generation sequencing reads data.","authors":"Lin Wan, Xin Kang, Jie Ren, Fengzhu Sun","doi":"10.1007/s40484-020-0200-y","DOIUrl":null,"url":null,"abstract":"<p><strong>Background: </strong>Markov chains (MC) have been widely used to model molecular sequences. The estimations of MC transition matrix and confidence intervals of the transition probabilities from long sequence data have been intensively studied in the past decades. In next generation sequencing (NGS), a large amount of short reads are generated. These short reads can overlap and some regions of the genome may not be sequenced resulting in a new type of data. Based on NGS data, the transition probabilities of MC can be estimated by moment estimators. However, the classical asymptotic distribution theory for MC transition probability estimators based on long sequences is no longer valid.</p><p><strong>Methods: </strong>In this study, we present the asymptotic distributions of several statistics related to MC based on NGS data. We show that, after scaling by the effective coverage <i>d</i> defined in a previous study by the authors, these statistics based on NGS data approximate to the same distributions as the corresponding statistics for long sequences.</p><p><strong>Results: </strong>We apply the asymptotic properties of these statistics for finding the theoretical confidence regions for MC transition probabilities based on NGS short reads data. We validate our theoretical confidence intervals using both simulated data and real data sets, and compare the results with those by the parametric bootstrap method.</p><p><strong>Conclusions: </strong>We find that the asymptotic distributions of these statistics and the theoretical confidence intervals of transition probabilities based on NGS data given in this study are highly accurate, providing a powerful tool for NGS data analysis.</p>","PeriodicalId":45660,"journal":{"name":"Quantitative Biology","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40484-020-0200-y","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantitative Biology","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1007/s40484-020-0200-y","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/5/25 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
引用次数: 1
Abstract
Background: Markov chains (MC) have been widely used to model molecular sequences. The estimations of MC transition matrix and confidence intervals of the transition probabilities from long sequence data have been intensively studied in the past decades. In next generation sequencing (NGS), a large amount of short reads are generated. These short reads can overlap and some regions of the genome may not be sequenced resulting in a new type of data. Based on NGS data, the transition probabilities of MC can be estimated by moment estimators. However, the classical asymptotic distribution theory for MC transition probability estimators based on long sequences is no longer valid.
Methods: In this study, we present the asymptotic distributions of several statistics related to MC based on NGS data. We show that, after scaling by the effective coverage d defined in a previous study by the authors, these statistics based on NGS data approximate to the same distributions as the corresponding statistics for long sequences.
Results: We apply the asymptotic properties of these statistics for finding the theoretical confidence regions for MC transition probabilities based on NGS short reads data. We validate our theoretical confidence intervals using both simulated data and real data sets, and compare the results with those by the parametric bootstrap method.
Conclusions: We find that the asymptotic distributions of these statistics and the theoretical confidence intervals of transition probabilities based on NGS data given in this study are highly accurate, providing a powerful tool for NGS data analysis.
期刊介绍:
Quantitative Biology is an interdisciplinary journal that focuses on original research that uses quantitative approaches and technologies to analyze and integrate biological systems, construct and model engineered life systems, and gain a deeper understanding of the life sciences. It aims to provide a platform for not only the analysis but also the integration and construction of biological systems. It is a quarterly journal seeking to provide an inter- and multi-disciplinary forum for a broad blend of peer-reviewed academic papers in order to promote rapid communication and exchange between scientists in the East and the West. The content of Quantitative Biology will mainly focus on the two broad and related areas: ·bioinformatics and computational biology, which focuses on dealing with information technologies and computational methodologies that can efficiently and accurately manipulate –omics data and transform molecular information into biological knowledge. ·systems and synthetic biology, which focuses on complex interactions in biological systems and the emergent functional properties, and on the design and construction of new biological functions and systems. Its goal is to reflect the significant advances made in quantitatively investigating and modeling both natural and engineered life systems at the molecular and higher levels. The journal particularly encourages original papers that link novel theory with cutting-edge experiments, especially in the newly emerging and multi-disciplinary areas of research. The journal also welcomes high-quality reviews and perspective articles.