Description
This talk focuses on parameter estimation in Bayesian inverse problems, where a physical model governed by differential equations is combined with noisy data. A key difficulty is the presence of discretization bias and intractable likelihoods, which hinder reliable inference. I present a methodology that delivers unbiased stochastic estimators of optimal parameters by combining stochastic approximation and modern debiasing techniques. The approach removes numerical bias while remaining computationally efficient. Theoretical guarantees and numerical results on PDE and ODE models demonstrate clear improvements over existing methods.