Optimal convergence rates of MCMC integration for functions with unbounded second moment
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912533515862016 |
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| author | Hofstadler, Julian |
| author_facet | Hofstadler, Julian |
| contents | We study the Markov chain Monte Carlo (MCMC) estimator for numerical integration for functions that do not need to be square integrable w.r.t. the invariant distribution. For chains with a spectral gap we show that the absolute mean error for $L^p$ functions, with $p \in (1,2)$, decreases like $n^{1/p -1}$, which is known to be the optimal rate. This improves currently known results where an additional parameter $δ>0$ appears and the convergence is of order $n^{(1+δ)/p-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal convergence rates of MCMC integration for functions with unbounded second moment Hofstadler, Julian Numerical Analysis 65C05, 60J22, 65C20 We study the Markov chain Monte Carlo (MCMC) estimator for numerical integration for functions that do not need to be square integrable w.r.t. the invariant distribution. For chains with a spectral gap we show that the absolute mean error for $L^p$ functions, with $p \in (1,2)$, decreases like $n^{1/p -1}$, which is known to be the optimal rate. This improves currently known results where an additional parameter $δ>0$ appears and the convergence is of order $n^{(1+δ)/p-1}$. |
| title | Optimal convergence rates of MCMC integration for functions with unbounded second moment |
| topic | Numerical Analysis 65C05, 60J22, 65C20 |
| url | https://arxiv.org/abs/2403.16920 |