Learning Bayes' theorem with a neural network for gravitational-wave inference
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We wish to achieve the Holy Grail of Bayesian inference with deep-learning techniques: training a neural network to instantly produce the posterior p(θ|D) for the parameters θ, given the data D. In the setting of gravitational-wave astronomy, we have access to a generative model for signals in noisy data (i.e., we can instantiate the prior p(θ) and likelihood p(D|θ)), but are unable to economically compute the posterior for even a single realization of D. Here we demonstrate how a network may be taught to estimate p(θ|D) regardless, by simply showing it numerous realizations of D.
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