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| Wielopoziomowe Monte Carlo Hamiltona× | Wielopoziomowe MCMC× | |
|---|---|---|
| Dziedzina | Statystyka bayesowska | Statystyka bayesowska |
| Rodzina | Bayesian methods | Bayesian methods |
| Rok powstania≠ | 2010s | 1990s |
| Twórca≠ | Beskos, Jasra, Law, Tempone, Zhou (multilevel MCMC); Neal (HMC component) | Gelfand & Smith (sampling-based approach); multilevel extension developed through 1990s Bayesian hierarchical modeling literature |
| Typ≠ | Bayesian computational sampler | Bayesian computational inference |
| Źródło pierwotne≠ | Beskos, A., Jasra, A., Law, K., Tempone, R., & Zhou, Y. (2017). Multilevel sequential Monte Carlo samplers. Stochastic Processes and their Applications, 127(5), 1417–1440. DOI ↗ | Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955 |
| Inne nazwy | Multilevel HMC, MLHMC, multilevel HMC sampler, multilevel leapfrog MCMC | hierarchical MCMC, multilevel Bayesian sampling, MLMCMC, hierarchical Markov chain Monte Carlo |
| Pokrewne≠ | 5 | 6 |
| Podsumowanie≠ | Multilevel Hamiltonian Monte Carlo (Multilevel HMC) combines the variance-reduction strategy of multilevel Monte Carlo with the efficient gradient-driven exploration of Hamiltonian Monte Carlo. By running coupled HMC chains at increasing levels of model fidelity or discretisation, it achieves accurate posterior estimates at a computational cost substantially lower than a single fine-level HMC chain. | Multilevel MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty across levels and enabling inference in clustered or nested data structures where observations within groups share common distributional characteristics. |
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