Approximating conditional distributions
Probability
2017-10-25 v1
Abstract
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose solution can be bounded, for example, via ad hoc couplings. This method provides quantitative bounds in several examples: the filtering equation, the distance between bridges of random walks and the distance between bridges and discrete schemes approximating them. Moreover, through the coupling construction for a certain class of random walk bridges we determine samplers, whose convergence to equilibrium is computed explicitly.
Cite
@article{arxiv.1710.08856,
title = {Approximating conditional distributions},
author = {Alberto Chiarini and Alessandra Cipriani and Giovanni Conforti},
journal= {arXiv preprint arXiv:1710.08856},
year = {2017}
}