On the Pitfalls of Nested Monte Carlo

Abstract

There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for which classical convergence proofs are insufficient. We give conditions under which NMC will converge, establish a rate of convergence, and provide empirical data that suggests that this rate is observable in practice. Finally, we prove that general-purpose nested inference schemes are inherently biased. Our results serve to warn of the dangers associated with naive composition of inference and models.

arXiv commentAppearing in NIPS Workshop on Advances in Approximate Bayesian Inference 2016

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Cited by in corpus (3)

• Unbiased estimation of log normalizing constants with applications to Bayesian cross-validation
• Nesting Probabilistic Programs
• An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions