Abstract

Introduction

In many situations, understanding the behaviour of a stochastic system is greatly aided by understanding its behaviour conditioned on certain events. This allows us, for example, to study rare events by conditioning on the event happening or to analyse the behaviour of a composite system when only some of its components can be observed. Since properties of conditional distributions are often difficult to obtain analytically, it is desirable to be able to study these distributions numerically. This allows us to develop meaningful conjectures about the distribution in question or, in a more applied context, to derive quantitative information about it. In this text we present a general technique to generate samples from conditional distributions on infinite-dimensional spaces. We give several examples to illustrate how this technique can be applied.

Sampling, i.e. finding a mechanism which produces random values distributed according to a prescribed target distribution, is generally a difficult problem. There exist many ‘tricks’ to sample from specific distributions, ranging from very specialized methods, like the Box–Müller method for generating one-dimensional standard Gaussian distributed values, to generic methods, like rejection sampling, which can be applied to whole classes of distributions.