AeMCMC

1 min read

https://github.com/aesara-devs/aemcmc

Based on the intermediate representation built by AePPL:

  • Built upon representation in terms of measures
  • NUTS as default
  • Gibbs samplers
  • Closed-form posterior
  • Reversible jump
  • Walk the space of equivalent representations of the graph
  • Automatic inference
  • Specify that we want a specific sampler from
  • Specify that we don’t want some samplers
import aemcmc
import aesara
import aesara.tensor as at
 
srng = at.random.RandomStream(0)
 
X = at.matrix("X")
 
# Horseshoe prior for `beta_rv`
tau_rv = srng.halfcauchy(0, 1, name="tau")
lmbda_rv = srng.halfcauchy(0, 1, size=X.shape[1], name="lambda")
beta_rv = srng.normal(0, lmbda_rv * tau_rv, size=X.shape[1], name="beta")
 
a = at.scalar("a")
b = at.scalar("b")
h_rv = srng.gamma(a, b, name="h")
 
# Negative-binomial regression
eta = X @ beta_rv
p = at.sigmoid(-eta)
Y_rv = srng.nbinom(h_rv, p, name="Y")
 
y_vv = Y_rv.clone()
y_vv.name = "y"
 
sampler, initial_values = aemcmc.construct_sampler({Y_rv: y_vv}, srng)
 
print(sampler.sample_steps[h_rv])
print(sampler.stages)

Rewrites on the logprob

We’ve discussed this and it should happen, as some people will have bad geometry that’s induced by a big function they’re using. (see models used by Marcus who wrote the MUSE paper)

Using copulas

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