השוואת שיטות
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| המילטוניאן מונטה קרלו× | הסקה בייסיאנית היררכית× | |
|---|---|---|
| תחום | בייסיאני | בייסיאני |
| משפחה | Bayesian methods | Bayesian methods |
| שנת המקור≠ | 1987 | 1972 (Lindley & Smith); consolidated 1995–2013 |
| הוגה השיטה≠ | — | Lindley & Smith; Gelman et al. |
| סוג≠ | Gradient-based Markov chain Monte Carlo sampler | Bayesian multilevel model |
| מקור מכונן≠ | Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222. 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 |
| כינויים≠ | HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler | multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model |
| קשורות≠ | 3 | 6 |
| תקציר≠ | Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models. | Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate. |
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