Approximating conditional distributions

Alberto Chiarini; Alessandra Cipriani; Giovanni Conforti

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arXiv · 1710.08856

Approximating conditional distributions

Alberto Chiarini·Alessandra Cipriani·Giovanni Conforti

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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.

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Alberto Chiarini, Alessandra Cipriani, Giovanni Conforti. 2017-10-24. Approximating conditional distributions. https://arxiv.org/abs/1710.08856

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