Contributions on metric spaces with applications in personalized medicine

This thesis aims to propose new distributional representations and statistical methods in metric spaces to efficiently model biosensor times series when the patients are monitored in free-living conditions. We propose new hypothesis tests for paired data, regression models, uncertainty quantification algorithms, statistical independence tests, and cluster analysis algorithms for the new distributional representations and other complex statistical objects. The results collected throughout the thesis show the advantages of the new proposals over existing methods in predicting, interpreting, and capturing relevant clinical information in the case of continuous glucose monitors and accelerometer devices.