Home > Research > Publications & Outputs > Variance bounding of delayed-acceptance kernels

Electronic data

  • davb_1_3_arxiv

    Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-021-09914-1

    Accepted author manuscript, 396 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

View graph of relations

Variance bounding of delayed-acceptance kernels

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
<mark>Journal publication date</mark>22/11/2021
<mark>Journal</mark>Methodology and Computing in Applied Probability
Publication StatusE-pub ahead of print
Early online date22/11/21
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-021-09914-1