Methoden vergleichen
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| Markov-Kette Monte Carlo (MCMC)× | Mixed Effects Model× | Ridge Regression× | |
|---|---|---|---|
| Fachgebiet≠ | Bayes-Statistik | Statistik | Maschinelles Lernen |
| Familie≠ | Bayesian methods | Regression model | Machine learning |
| Entstehungsjahr≠ | — | 1982 | 1970 |
| Urheber≠ | — | Laird & Ware | Hoerl, A.E. & Kennard, R.W. |
| Typ≠ | Posterior sampling algorithm | Mixed effects regression | L2-regularized linear regression |
| Wegweisende Quelle≠ | 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 | Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974. DOI ↗ | Hoerl, A.E. & Kennard, R.W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12(1), 55–67. DOI ↗ |
| Aliasnamen≠ | markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo) | LME, LMM, mixed model, random effects model | Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization |
| Verwandt≠ | 3 | 4 | 4 |
| Zusammenfassung≠ | Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model. | A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated. | Ridge Regression is an L2-regularized linear regression method, introduced by Arthur Hoerl and Robert Kennard in 1970, that reduces multicollinearity by adding a penalty on the size of the coefficients. It shrinks coefficients toward zero without setting any of them exactly to zero, producing more stable estimates when predictors are highly correlated. |
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