  Phenotypic variability in a population of cells can work as the bet-hedging
of the cells under an unpredictably changing environment, the typical example
of which is the bacterial persistence. To understand the strategy to control
such phenomena, it is indispensable to identify the phenotype of each cell and
its inheritance. Although recent advancements in microfluidic technology offer
us useful lineage data, they are insufficient to directly identify the
phenotypes of the cells. An alternative approach is to infer the phenotype from
the lineage data by latent-variable estimation. To this end, however, we must
resolve the bias problem in the inference from lineage called survivorship
bias. In this work, we clarify how the survivor bias distorts statistical
estimations. We then propose a latent-variable estimation algorithm without the
survivorship bias from lineage trees based on an expectation-maximization (EM)
algorithm, which we call Lineage EM algorithm (LEM). LEM provides a statistical
method to identify the traits of the cells applicable to various kinds of
lineage data.
