Exact probability of fixed patterns occurring in a random sequence

• Published in: Communications in statistics. Simulation and computation Vol. 51; no. 9; pp. 4867 - 4882
• Main Authors: Sheng, Ke-Ning, Naus, Joseph I.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 27-09-2022; Taylor & Francis Ltd
• Subjects: Anthropology; Clinical medicine; Data mining; Molecular biology; Partially occurring group; Pattern analysis; Pattern recognition; Recurrence relation; Relation equation
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2020.1766500

We derive a procedure to obtain the exact probability that a specific pattern of letters occurs in a longer random sequence of letters. The procedure is generalized to find the exact probability of a fixed (specific) single pattern, and a union or intersection of multiple fixed (specific) patterns within a random sequence perfectly for any distributions of a cell in the random sequence, and can handle patterns with uncertain letters (including missing, blank, unclear, ambiguous, transposition, etc.). The procedure also finds the probability that a pattern that is randomly picked will appear in a separate longer random sequence of letters. These methods are of particular applicability in genetic sequence analysis, diagnostics, anthropology, clinical medicine, data mining, computational molecular biology, and pattern analysis and recognition.