Explore statistical physics and statistical inference in this comprehensive lecture by Marc Mézard, Director of Ecole normale supérieure - PSL University. Delve into Bayesian inference, error-correcting codes, and phase transitions in spin glasses. Examine crystal hunting algorithms, belief propagation, and mean-field equations. Investigate applications in compressed sensing, perceptron learning, and generalized linear regression. Learn about message passing algorithms, TAP equations, and strategies for overcoming glass traps in optimization problems. Gain insights into the connections between statistical physics and machine learning through this in-depth presentation, which includes a Q&A session.