Mueller polarimetry is increasingly recognized as a powerful modality in biomedical imaging. Nevertheless, principled statistical analysis procedures are still lacking in this field. This paper presents a complete pipeline for polarimetric bioimages, with an application to ex vivo cervical precancer detection. In the preprocessing stage, we evaluate the replacement of pixels by superpixels. In the analysis stage, we resort to decision theory to select and tune a classifier. Performances of the retained classifier are evaluated. Decision theory provides a rigorous and versatile framework, allowing generalization to other pathologies, to other imaging procedures, and to classification problems involving more than two classes.