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FR rules for (Gaussian + UniformPolygon).reduce(logaddexp) #596

Description

@fritzo

It would be great to have reduction rules for uniform likelihoods wrt Gaussian latent variables:

  • (MyContinuousDist + Uniform).reduce(logaddexp) implemented via .cdf()
  • (Gaussian + UniformPolygon).reduce(logaddexp) implemented via quadrature (MC or QMC)

This could be used for Pyro and NumPyro probabilistic programs with constraint-like likelihoods, something like

def model(data):
    z = pyro.sample("z", Normal(...))
    # Observe a constraint like lb < z < ub.
    pyro.sample("x", Uniform(...), obs=z)

here we can be lazy and compute marginal likelihood via Normal(...).cdf([lb, ub]).

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