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Technological challenges >> Numerical simulation
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Approximate Bayesian inference based on stochastic simulation

Département Métrologie Instrumentation et Information (LIST)

Laboratoire Modélisation et Simulation des Systèmes



In many scientific fields, from particle physics to cosmology, including molecular biology and epidemiology, it is now common practice to develop simulation tools in order to describe complex phenomena. These simulation-based models are often stochastic (Monte Carlo) and have multiple input parameters. While the primary object of stochastic simulation is to be able to generate data from a configuration of parameters (forward simulation), its practical interest often resides in the opposite problem: determining a configuration of parameters of the model making it possible to generate data sufficiently close to those observed in Nature. Knowledge of these parameters can then represent the objective of the study or be used to calibrate the simulator for subsequent analyzes. However, solving such a nonlinear and very indirect problem is in general a difficult task. Our goal is to build a rigorous statistical inference framework for estimating these parameters. In particular, we propose to adopt the Bayesian paradigm for the resolution of the inverse problem in order to characterize the set of solutions via their a posteriori distribution. However, this objective comes up against a fundamental difficulty here: we do not have the analytical expression of likelihood in the context of stochastic simulation (likelihood free). This challenge has recently appeared to be amenable thanks to the emergence of two complementary techniques: ABC (Approximate Bayesian Computation) and deep generative models. As part of this project, we propose to evaluate the feasibility of this approach in an application scenario in the field of stochastic particle transport.

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