Establishing some order amongst exact approximations of MCMCs
Andrieu, C., & Vihola, M. (2016). Establishing some order amongst exact approximations of MCMCs. Annals of Applied Probability, 26(5), 2661-2696. https://doi.org/10.1214/15-AAP1158
Published in
Annals of Applied ProbabilityDate
2016Copyright
© Institute of Mathematical Statistics, 2016. Published in this repository with the kind permission of the publisher.
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms
are a general emerging class of sampling algorithms. One of the main
ideas behind exact approximations consists of replacing intractable quantities
required to run standard MCMC algorithms, such as the target probability
density in a Metropolis–Hastings algorithm, with estimators. Perhaps
surprisingly, such approximations lead to powerful algorithms which are exact
in the sense that they are guaranteed to have correct limiting distributions.
In this paper, we discover a general framework which allows one to compare,
or order, performance measures of two implementations of such algorithms.
In particular, we establish an order with respect to the mean acceptance probability,
the first autocorrelation coefficient, the asymptotic variance and the
right spectral gap. The key notion to guarantee the ordering is that of the convex
order between estimators used to implement the algorithms. We believe
that our convex order condition is close to optimal, and this is supported by
a counterexample which shows that a weaker variance order is not sufficient.
The convex order plays a central role by allowing us to construct a martingale
coupling which enables the comparison of performance measures of Markov
chain with differing invariant distributions, contrary to existing results. We
detail applications of our result by identifying extremal distributions within
given classes of approximations, by showing that averaging replicas improves
performance in a monotonic fashion and that stratification is guaranteed to
improve performance for the standard implementation of the Approximate
Bayesian Computation (ABC) MCMC method.
...
Publisher
Institute of Mathematical StatisticsISSN Search the Publication Forum
1050-5164Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/26285312
Metadata
Show full item recordCollections
Related funder(s)
Academy of FinlandFunding program(s)
Academy Research Fellow, AoFRelated items
Showing items with similar title or keywords.
-
On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction
Vihola, Matti; Franks, Jordan (Oxford University Press, 2020)Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation ... -
Statistical analysis of β decays and the effective value of gA in the proton-neutron quasiparticle random-phase approximation framework
Deppisch, Frank F.; Suhonen, Jouni (American Physical Society, 2016)We perform a Markov chain Monte Carlo (MCMC) statistical analysis of a number of measured groundstate-to-ground-state single β+/electron-capture and β− decays in the nuclear mass range of A = 62–142. The corresponding ... -
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
Vihola, Matti; Helske, Jouni; Franks, Jordan (Wiley-Blackwell, 2020)We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the ... -
Part-of-speech tagging in written slang
Korolainen, Valtteri (2014)Erilaiset kieliteknologiasovellukset ovat olleet jo vuosikymmeniä arkipäiväises-sä käytössä. Esimerkiksi ennustava tekstinsyöttö ja automaattinen korjaus ovat olleet käytössä jo vuosikymmeniä. Puheen tunnistus ja kielen ... -
Optimization of Linearized Belief Propagation for Distributed Detection
Abdi, Younes; Ristaniemi, Tapani (IEEE, 2020)In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP ...