The MDN is one of the neural density estimators in neuralsbi (the default
is the MAF, matching Python sbi). A multilayer
perceptron maps the data x to the parameters of a Gaussian mixture over the
parameters \(\theta\): mixture logits, component means, and (full)
lower-triangular Cholesky factors of each component covariance. Training
minimizes the negative log-likelihood of \(\theta\) under the mixture,
which – when simulations are drawn from the prior – yields a direct
amortized approximation of the posterior \(p(\theta \mid x)\).