Let’s think about a likelihood which is non-trivial y=(x+\mu+\sigma\epsilon)^2,\ \text{with}\ \epsilon\sim\mathcal{N}(0,1) I know this can be transformed into ChiSquared dist analytically. But we still will encounter more complicated and non-linear function (maybe deep nerual network!!) involving…

Trivial stuff PyMC CustomDist can do it for you. Borrowing your example: import pymc as pm def dist(mu, sigma, size): return (mu + sigma * pm.Normal.dist(size=size)) ** 2 mu = 2 sigma = 1.5 x1 = pm.CustomDist.dist(mu, sigma, dist=dist) value = 0.7 print(pm.logp(x1, value).eval()) # -1.9362354…

Finally, I choose to use approximate bayesian computation (ABC), like using kernel density estimate (KDE) to calculate likelihood approximately.

How to model very complicated likelihood automatically？

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How to model very complicated likelihood automatically？

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