February 19, 2024Open Access

Almost sure convergence rates of adaptive increasingly rare Markov chain Monte Carlo

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Authors

JHJulian HofstadlerUniversity of Bath KŁKrzysztof ŁatuszyńskiUniversity of Warwick GRGareth O. RobertsUniversity of Warwick

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Implication

Theoretical analysis demonstrates almost sure convergence rates for adaptive MCMC, highlighting asymptotic validity without standard diminishing adaptation assumptions.

Key Points

Upper bounds on convergence rates for adaptive increasingly rare Markov chain Monte Carlo hold under a contraction assumption for a Wasserstein-like function.
Monte Carlo sums scale with a renormalisation factor close to the law of the iterated logarithm, demonstrating applicability in uniform ergodicity settings.
Theoretical proofs on an augmented state space confirm that convergence guarantees hold firmly without requiring traditional diminishing adaptation assumptions.

Cite This Study

Hofstadler et al. (2024) studied this question.

synapsesocial.com/papers/68e78a60b6db6435876fcd12 https://doi.org/10.48550/arxiv.2402.12122

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Implication

Theoretical analysis demonstrates almost sure convergence rates for adaptive MCMC, highlighting asymptotic validity without standard diminishing adaptation assumptions.

Almost sure convergence rates of adaptive increasingly rare Markov chain Monte Carlo

Discussion

Member takes

Implication

Key Points

Cite This Study

Almost sure convergence rates of adaptive increasingly rare Markov chain Monte Carlo

Discussion

Member takes

Implication

Key Points

Cite This Study

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