  Contamination of water resources with pathogenic microorganisms excreted in
human feces is a worldwide public health concern. Surveillance of fecal
contamination is commonly performed by routine monitoring for a single type or
a few types of microorganism(s). To design a feasible routine for periodic
monitoring and to control risks of exposure to pathogens, reliable statistical
algorithms for inferring correlations between concentrations of microorganisms
in water need to be established. Moreover, because pathogens are often present
in low concentrations, some contaminations are likely to be under a detection
limit. This yields a pairwise left-censored dataset and complicates computation
of correlation coefficients. Errors of correlation estimation can be smaller if
undetected values are imputed better. To obtain better imputations, we utilize
side information and develop a new technique, the \emph{asymmetric Tobit model}
which is an extension of the Tobit model so that domain knowledge can be
exploited effectively when fitting the model to a censored dataset. The
empirical results demonstrate that imputation with domain knowledge is
effective for this task.
