ArXiv Preprint
Monitoring microbiological behaviors in water is crucial to manage public
health risk from waterborne pathogens, although quantifying the concentrations
of microbiological organisms in water is still challenging because
concentrations of many pathogens in water samples may often be below the
quantification limit, producing censoring data. To enable statistical analysis
based on quantitative values, the true values of non-detected measurements are
required to be estimated with high precision. Tobit model is a well-known
linear regression model for analyzing censored data. One drawback of the Tobit
model is that only the target variable is allowed to be censored. In this
study, we devised a novel extension of the classical Tobit model, called the
\emph{multi-target Tobit model}, to handle multiple censored variables
simultaneously by introducing multiple target variables. For fitting the new
model, a numerical stable optimization algorithm was developed based on
elaborate theories. Experiments conducted using several real-world water
quality datasets provided an evidence that estimating multiple columns jointly
gains a great advantage over estimating them separately.
Yuya Takada, Tsuyoshi Kato
2023-02-21
