Ricerc@Sapienza

Within a Bayesian framework, the main goal of this project is to systematically investigate the use of optimal transportation methods in the design of statistical experiments, with a particular emphasis towards applications to sample size determination and planning of (possibly) high-dimensional clinical trials.

Optimal transport (OT) distances between probability measures in general, and the family of Wasserstein distances more in particular, have a long and well established history in probability theory. In more recent years, they have also found their way into statistical theory, applications and machine learning, not only as a theoretical tool but also as a quantity of interest in its own right. A non-exhaustive list of examples include goodness-of-fit, two-sample and equivalence testing; classification and clustering; exploratory data analysis via Frechet means and geodesics in the Wasserstein metric.

Despite this overflow of interest in OT, as today, its use and usefulness in the broad area of statistical experimental design seems to be only marginally explored.
Experimental design involves the specification of all aspects of an experiment, and decisions must be taken before data collection, usually under resource constraints. For this reason, at the design level, it is crucial to efficiently exploit all the relevant information available prior to experimentation, making Bayesian methods central.

Historically, the decision theoretic approach to (Bayesian) experimental design has been dominated by information criteria like Fisher information metric and Kullback-Leibler divergence, but recent developments suggest that, if we are willing to pay a small computational overhead, we can switch to the OT framework inheriting its robustness, shape preservation property and sensitivity to the underlying geometry without losing the original interpretability.
An extensive exploration of this idea in a variety of specific contexts is the leading theme of our proposal.