Probabilistic and statistical properties of words: an overview

Area of Science:

• Bioinformatics
• Computational Biology
• Statistical Genomics

Background:

• Analyzing biological sequences involves understanding word occurrences and their statistical properties.
• Accurate statistical models are crucial for interpreting complex biological sequence data.

Purpose of the Study:

• To provide an overview of statistical and probabilistic properties of words in biological sequence analysis.
• To develop methods for analyzing word occurrences, including exact distributions and various approximations.
• To address the challenges of dependence structures between word occurrences and sequence recoverability.

Main Methods:

• Modeling biological sequences as stationary ergodic Markov chains.
• Deriving exact distributions and approximations (normal, Poisson, compound Poisson) for word counts.
• Utilizing moment generating functions, martingales, Stein's method, and the Chen-Stein method.
• Developing a test for determining Markov chain order and accounting for estimation errors.

Main Results:

• Distinguished counts of occurrence, clumps, and renewals with derived distributions and approximations.
• Established convergence results considering estimation errors in Markovian transition probabilities.
• Provided methods for analyzing multiple pattern occurrences and sequence recoverability from SBH chip data.
• Disentangled complex dependence structures between word occurrences due to self-overlap and inter-word overlap.

Conclusions:

• The developed statistical methods offer accurate and conservative confidence intervals for hypothesis testing in biological sequence analysis.
• The study enhances the understanding of word patterns in biological sequences, aiding in data interpretation.
• The findings are applicable to various bioinformatics problems, including sequence assembly and analysis of high-throughput sequencing data.