Statistical Analysis of DNA Sequences Using Overlapping Windows

Motivation: Our analysis of DNA sequences uses a k-length, sliding window and considers all overlapping windows along the sequence. The k consecutive nucleotides in a window are called a word or k-word. Statistical analysis of this collection of words often assumes independence between words. Since words can overlap, strict independence is not a valid assumption. We derive a statistic to incorporate both the independent and dependent components of overlapping, k-length words. Results: The expected number of occurrences for a k-word in an N-length sequence is easily calculated given the probabilities of the nucleotides within the word. However, the variance is not straightforward since overlapping occurrences are not independent. We present a derivation of the variance when sequence analysis uses overlapping, k-length windows. The variance can be determined for a word in the entire sequence or at a single position in the sequence. Our analysis assumes that each nucleotide is independent. It does not assume a specific probability of occurrence for each nucleotide.

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