How to Calculate Substitution, Insertion, and Deletion Probabilities for Fixed Sequences

• Activity Number: 349
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 11:15 AM
• Sponsor: Social Statistics Section
• Author(s): Jason Wilson*+
• Companies: Biola University
• Keywords: probability ; Bible ; substitution ; insertion ; deletion ; sequence

Abstract

Fixed sequences occur in many places - books, movies, genomes, and so on. We will look at the probability of the three different types of error which may occur when a fixed sequence is copied: substitution, insertion, and deletion. One general formula is shown to compute the conditional probability for all three types of error. The unconditional probability calculation follows. Three real examples will be considered: an online streaming skip from Star Wars, a potential ancient manuscript insertion into the Gospel of Luke in the Bible, and a genetic substitution (mutation) resulting in sickle cell anemia. With this background, the most interesting part of the paper is the extraction of general interpretive principles regarding: How do the conditional vs. unconditional probabilities effect the interpretation? How should we think about the extremely small probabilities obtained? How do we decide whether or not an event should be considered a coincidence?