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Error bounds for Approximations of Markov chains. (arXiv:1711.05382v1 [math.PR])
来源于:arXiv
The first part of this article gives error bounds for approximations of
Markov kernels under Foster-Lyapunov conditions. The basic idea is that when
both the approximating kernel and the original kernel satisfy a Foster-Lyapunov
condition, the long-time dynamics of the two chains -- as well as the invariant
measures, when they exist -- will be close in a weighted total variation norm,
provided that the approximation is sufficiently accurate. The required accuracy
depends in part on the Lyapunov function, with more stable chains being more
tolerant of approximation error.
We are motivated by the recent growth in proposals for scaling Markov chain
Monte Carlo algorithms to large datasets by defining an approximating kernel
that is faster to sample from. Many of these proposals use only a small subset
of the data points to construct the transition kernel, and we consider an
application to this class of approximating kernel. We also consider
applications to distribution approximations in G 查看全文>>