Variance bounding of delayed-acceptance kernels

Sherlock, Chris and Lee, Anthony (2022) Variance bounding of delayed-acceptance kernels. Methodology and Computing in Applied Probability, 24 (3). pp. 2237-2260. ISSN 1387-5841

[thumbnail of davb_1_3_arxiv]
Text (davb_1_3_arxiv)
davb_1_3_arxiv.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (405kB)


A delayed-acceptance version of a Metropolis–Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheap approximation is available; the delayed-acceptance kernel targets the same posterior as its associated “parent” Metropolis-Hastings kernel. Although the asymptotic variance of the ergodic average of any functional of the delayed-acceptance chain cannot be less than that obtained using its parent, the average computational time per iteration can be much smaller and so for a given computational budget the delayed-acceptance kernel can be more efficient. When the asymptotic variance of the ergodic averages of all $L^2$ functionals of the chain are finite, the kernel is said to be variance bounding. It has recently been noted that a delayed-acceptance kernel need not be variance bounding even when its parent is. We provide sufficient conditions for inheritance: for non-local algorithms, such as the independence sampler, the discrepancy between the log density of the approximation and that of the truth should be bounded; for local algorithms, two alternative sets of conditions are provided. As a by-product of our initial, general result we also supply sufficient conditions on any pair of proposals such that, for any shared target distribution, if a Metropolis-Hastings kernel using one of the proposals is variance bounding then so is the Metropolis-Hastings kernel using the other proposal.

Item Type:
Journal Article
Journal or Publication Title:
Methodology and Computing in Applied Probability
Additional Information:
The final publication is available at Springer via
Uncontrolled Keywords:
?? metropolis-hastingsdelayed-acceptancevariance boundingconductancestatistics and probabilitymathematics(all) ??
ID Code:
Deposited By:
Deposited On:
18 Nov 2021 10:26
Last Modified:
04 Dec 2023 01:25