Unbiased Monte Carlo: posterior estimation for intractable/infinite-dimensional models

Understand

We provide a general methodology for unbiased estimation for intractable stochastic models.

• We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches require truncation of such a representation leading to a systematic bias.
• For example, the target distribution might be representable as the $L^2$-limit of a basis expansion in a suitable Hilbert space; or alternatively the distribution of interest might be representable as the weak limit of a sequence of random variables, as in MCMC.
• Our main motivation comes from infinite-dimensional models which can be parame- terised in terms of a series expansion of basis functions (such as that given by a Karhunen-Loeve expansion).