Inferential statistic as opposed to exploratory data analysis is essentially based on three types of models: parametric, non parametric and semi-parametric. Each of them has its proper qualities and drawbacks. The first type needs to be robustified [1], which means that the statistical performances have to be optimized not for the model itself but for a neighborhood of the model. This leads to minimax procedures, i.e. minimizing the maximum risk on the neighborhood. To define the adequate neighborhoods, some distances on probability spaces have to be chosen. Also for the second type of model, which has the advantage of leaving more freedom to the function to be estimated, no longer bounded to be defined up to a finite number of real parameters, but pertaining to a set of functions meeting some regularity condition, distances are chosen to define the minimax risk on this set [2,3]. This freedom for the function is at the cost of a more difficult interpretation. Most models in survival data analysis are of the third type: part of the model is free to be any function while another part implies parameters which will make sense to the user when the statistician announces the result. Relationships between distances are important [4]. Finally, when using neural networks algorithms, we come out (apparently) with "no model". I shall show some simple examples of robutsness, diagnosis, survival data analysis and comparison of prediction ability and explainability [5] of neural networks and classical statistics. REFERENCES [1] Huber C. "Théorie de la robustesse.(Theory of robustness)." Probability and statistics, Lecture Notes, Winter Sch., Santiago de Chile 1215: 1-128, (1986). [2] Bretagnolle J. et Huber C., « Estimation des densités : Risque minimax », Lecture notes in Mathematics, séminaire de Probabilités XII, vol. vol. 649, pp. 342–363, (1978) [3] Huber, C.. Lower bounds for function estimation. In Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics (pp. 245-258). New York, NY: Springer New York (1997). [4] Canonne, Clément L., « A short note on an inequality between KL and TV [archive] », arXiv.org, 15 (2022). [5] Huber, C. "From Risk Prediction to Risk Factors Interpretation. Comparison of Neural Networks and Classical Statistics for Dementia Prediction". arXiv :2301.06995 (2023).