Optimal Overlap Detection of Shotgun Reads

TL;DR

This paper analyzes the asymptotic error probabilities of optimal Bayesian detectors for overlap detection of shotgun reads in both noiseless and noisy settings, assuming stationarity and ergodicity of the underlying sequence.

Contribution

It provides exact characterizations of the asymptotic error probabilities for optimal overlap detection under various noise and sequence assumptions.

Findings

Exact asymptotic error probabilities derived for noiseless reads.

Exact asymptotic error probabilities derived for noisy reads with memoryless channels.

Results applicable to stationary and ergodic sequence models.

Abstract

We consider the problem of detecting the overlap between a pair of short fragments sampled in random locations from an exponentially longer sequence, via their possibly noisy reads. We consider a noiseless setting, in which the reads are noiseless, and the sequence is only assumed to be stationary and ergodic. Under mild conditions on the mixing property of the process generating the sequence, we characterize exactly the asymptotic error probability of the optimal Bayesian detector. Similarly, we consider a noisy setting, in which the reads are noisy versions of the sampled fragments obtained via a memoryless channel. We further assume that the sequence is stationary and memoryless, and similarly characterize exactly the asymptotic error probability of the optimal Bayesian detector for this case.