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Discover key insights in this French-language CRM-SSC Prize lecture that explores methods to overcome the "curse of dimensionality" through law interpolation techniques. Learn how law interpolation methods can be applied even when dimensionality is undefined within the abstract framework of Lebesgue integration, with practical applications in Bayesian data analysis. Gain an undergraduate-level introduction to integral approximation methods based on law interpolations, followed by recent findings comparing two families of law interpolation: MCMC approaches (parallel tempering, simulated tempering) and AIS/SMC approaches (Annealed Importance Sampling, Sequential Monte Carlo).
