Separate sequencing evidence from certainty about a variant

Define the evidence

A sequence read is an observation, not automatically an independent cell or error-free genome. Repeated copies of one starting molecule, shared preparation artifacts or correlated calling errors can make nominally separate reads dependent. A variant call also does not establish that a biological phenotype follows from the sequence.

Connect mechanism and measurement

The original calculation observes an event: at least three of four independent reads report the variant token. Under the error-only model each read reports it with probability e. The event probability is 4e³(1−e)+e⁴, combining exactly three and exactly four calls. Under a stipulated alternative, the call probability is 0.5, giving event likelihood 0.3125. Neither model is claimed to represent an actual sequencing platform.

The likelihood ratio divides the alternative event probability by the error-only event probability. To obtain a posterior within these two models, multiply each likelihood by its prior model probability and normalize. With alternative prior p, posterior is pL1/[pL1+(1−p)L0]. A likelihood alone is not a posterior and cannot choose its own prior.

Unmodeled contamination, correlated errors and intermediate variant fractions remain possible. If all reads are perfectly correlated, the four-read binomial calculation is not justified. The lesson supports bounded interpretation of supplied evidence, not pathogen detection, diagnosis, genome engineering or clinical susceptibility decisions.

Reconstruct the original record

At error probability 0.1, the error-only event likelihood is 4×0.001×0.9+0.0001=0.0037. The alternative likelihood is 0.3125, a ratio of about 84.4595. With equal prior model probabilities, the posterior alternative probability is 0.3125/(0.3125+0.0037)≈0.9882985, conditional on this limited model set and independence.

Predict and investigate

Predict first: Why can a strong likelihood ratio still fail to justify certainty or a causal phenotype claim?

Recompute both event likelihoods and change the prior without changing read evidence. Explain one dependence or omitted-model limitation that could make this numerical posterior unsuitable for an actual record.

Defend a changed case

Apply the mechanism to a changed boundary

Use error probability 0.2 and equal priors. Compute the error-only likelihood and alternative posterior.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

L0=4×0.008×0.8+0.0016=0.0272. The equal-prior posterior is 0.3125/(0.3125+0.0272)≈0.9199293. The lower value reflects weaker evidence under the higher error probability, not a measured clinical probability.

Retain bounded evidence

Preserve original assumptions, first responses and feedback exposure in the Microbiology evidence workspace. All numerical records are original fictional evidence. No culture, genetic modification, transfer execution, resistance generation or personal clinical interpretation is requested. Actual independent practical competence is not established.

Primary mechanism context, checked 30 October 2026. Original teaching and fictional data; no copied operating procedures.