We propose an analysis and applications of sample pooling to the epidemiologic monitoring of COVID-19. We first introduce a model of the RT-qPCR process used to test for the presence of virus in a sample and construct a statistical model for the viral load in a typical infected individual inspired by large-scale clinical datasets. We present an application of group testing for the prevention of epidemic outbreak in closed connected communities. We then propose a method for the measure of the prevalence in a population taking into account the increased number of false negatives associated with the group testing method.

Five to ten percent of school-aged children display dysgraphia, a neuro-motor disorder that causes difficulties in handwriting, which becomes a handicap in the daily life of these children. Yet, the diagnosis of dysgraphia remains tedious, subjective and dependent to the language besides stepping in late in the schooling. We propose a pre-diagnosis tool for dysgraphia using drawings called graphomotor tests. These tests are recorded using graphical tablets. We evaluate several machine-learning models and compare them to build this tool. A database comprising 305 children from the region of Grenoble, including 43 children with dysgraphia, has been established and diagnosed by specialists using the BHK test, which is the gold standard for the diagnosis of dysgraphia in France. We performed tests of classification by extracting, correcting and selecting features from the raw data collected with the tablets and achieved a maximum accuracy of 73% with cross-validation for three models. These promising results highlight the relevance of graphomotor tests to diagnose dysgraphia earlier and more broadly.

The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have been proposed and are now well understood empirically, theoretical guarantees about their asymptotic behavior is rather sparse and most results are limited to the binary setting. We prove here theoretical guarantees in the valued settings. We show that under some mild conditions on the parameter space, and in an asymptotic regime where $\log (d)/n$ and $\log (n)/d$ tend to $0$ when $n$ and $d$ tend to infinity, (1) the maximum-likelihood estimate of the complete model (with known labels) is consistent and (2) the log-likelihood ratios are equivalent under the complete and observed (with unknown labels) models. This equivalence allows us to transfer the asymptotic consistency, and under mild conditions, asymptotic normality, to the maximum likelihood estimate under the observed model. Moreover, the variational estimator is also consistent and, under the same conditions, asymptotically normal.