Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Symmetry

Abstract

We revisit our earlier paper, with two of the coauthors, in which we proposed an unbiased and consistent estimator (Formula presented.) for an unknown mutation rate (Formula presented.) of microorganisms. Previously, we proved that the associated sequence of estimators (Formula presented.) converges to (Formula presented.) almost surely pointwise on a nonextinct set (Formula presented.). Here, we show that this sequence converges also in the mean square with respect to conditional probability measure (Formula presented.) and that, with respect to (Formula presented.) the estimator is asymptotically unbiased. We further assume that a microorganism can mutate or turn to a different variant of one of the two types. In particular, it can mean that bacteria under attack by a virus or chemical agent are either perishing or surviving, turning them to stronger variant. We propose estimators for their respective types and show that they are a.s. pointwise and (Formula presented.) -consistent and asymptotically unbiased with respect to measure (Formula presented.). © 2022 by the authors.

DOI

10.3390/sym14081701

Publication Date

2022

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