Aprendizaje Basado en Problemas: Estimación Óptima para evaluar una técnica de inversión basada en Monte Carlo

In this work, we propose, design, and implement a solution to a problem of evaluating a numerical method. This problem was conceived with the intention of applying the methodology of problem-based learning (PBL) in postgraduate students of a course called "Applied Mathematics to Indirect Measurements". The main objective is for the student to understand and relate several fundamental concepts that appear in the problem at hand, without adding additional complications in the development of the code. Therefore, a linear toy model with a single random variable is considered. The specific problem is the study of the performance of a sequential Monte Carlo (SMC) method, developed by the authors in the field of inverse problems, through the estimation of the method's tuning parameter. To do this, a supervised classification is proposed that use as training data those generated by the optimal estimation (OE) method. The idea of the work is that students, through the developed code, can analyze how the topics of two very important areas of applied mathematics today, namely, inverse problems (IP) and machine learning (ML), are integrated in practice through a Bayesian approach, such as the OE method.