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.

Many measurements in the physical sciences can be cast as counting experiments, where the number of occurrences of a physical phenomenon informs the prevalence of the phenomenon's source. Often, detection of the physical phenomenon (termed signal) is difficult to distinguish from naturally occurring phenomena (termed background). In this case, the discrimination of signal events from background can be performed using classifiers, and they may range from simple, threshold-based classifiers to sophisticated neural networks. These classifiers are often trained and validated to obtain optimal accuracy, however we show that the optimal accuracy classifier does not generally coincide with a classifier that provides the lowest detection limit, nor the lowest quantification uncertainty. We present a derivation of the detection limit and quantification uncertainty in the classifier-based counting experiment case. We also present a novel abstention mechanism to minimize the detection limit or quantification uncertainty \emph{a posteriori}. We illustrate the method on two data sets from the physical sciences, discriminating Ar-37 and Ar-39 radioactive decay from non-radioactive events in a gas proportional counter, and discriminating neutrons from photons in an inorganic scintillator and report results therefrom.

Methods of deep learning have become increasingly popular in recent years, but they have not arrived in compositional data analysis. Imputation methods for compositional data are typically applied on additive, centered or isometric log-ratio representations of the data. Generally, methods for compositional data analysis can only be applied to observed positive entries in a data matrix. Therefore one tries to impute missing values or measurements that were below a detection limit. In this paper, a new method for imputing rounded zeros based on artificial neural networks is shown and compared with conventional methods. We are also interested in the question whether for ANNs, a representation of the data in log-ratios for imputation purposes, is relevant. It can be shown, that ANNs are competitive or even performing better when imputing rounded zeros of data sets with moderate size. They deliver better results when data sets are big. Also, we can see that log-ratio transformations within the artificial neural network imputation procedure nevertheless help to improve the results. This proves that the theory of compositional data analysis and the fulfillment of all properties of compositional data analysis is still very important in the age of deep learning.

Finite mixture model is an important branch of clustering methods and can be applied on data sets with mixed types of variables. However, challenges exist in its applications. First, it typically relies on the EM algorithm which could be sensitive to the choice of initial values. Second, biomarkers subject to limits of detection (LOD) are common to encounter in clinical data, which brings censored variables into finite mixture model. Additionally, researchers are recently getting more interest in variable importance due to the increasing number of variables that become available for clustering. To address these challenges, we propose a Bayesian finite mixture model to simultaneously conduct variable selection, account for biomarker LOD and obtain clustering results. We took a Bayesian approach to obtain parameter estimates and the cluster membership to bypass the limitation of the EM algorithm. To account for LOD, we added one more step in Gibbs sampling to iteratively fill in biomarker values below or above LODs. In addition, we put a spike-and-slab type of prior on each variable to obtain variable importance. Simulations across various scenarios were conducted to examine the performance of this method. Real data application on electronic health records was also conducted.