  Inference metaprogramming enables effective probabilistic programming by
supporting the decomposition of executions of probabilistic programs into
subproblems and the deployment of hybrid probabilistic inference algorithms
that apply different probabilistic inference algorithms to different
subproblems. We introduce the concept of independent subproblem inference (as
opposed to entangled subproblem inference in which the subproblem inference
algorithm operates over the full program trace) and present a mathematical
framework for studying convergence properties of hybrid inference algorithms
that apply different Markov-Chain Monte Carlo algorithms to different parts of
the inference problem. We then use this formalism to prove asymptotic
convergence results for probablistic programs with inference metaprogramming.
To the best of our knowledge this is the first asymptotic convergence result
for hybrid probabilistic inference algorithms defined by (subproblem-based)
inference metaprogramming.
