Methoden vergleichen

	Metropolis-Hastings zur Modellvergleich	Sequentielle Monte-Carlo-Methoden
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1970 (extended 1995)	1993 (particle filter); 2006 (SMC samplers)
Urheber	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)	Gordon, Salmond & Smith (particle filter); Del Moral, Doucet & Jasra (SMC samplers)
Typ	MCMC-based model comparison	Sequential Bayesian computation
Wegweisende Quelle	Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97-109.	Gordon, N. J., Salmond, D. J., & Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F - Radar and Signal Processing, 140(2), 107–113.
Aliasnamen	MH model comparison, Metropolis-Hastings Bayes factor estimation, reversible-jump Metropolis-Hastings, MH model selection	SMC, particle filter, sequential importance resampling, SMC sampler
Verwandt	4	6
Zusammenfassung	Metropolis-Hastings for model comparison uses the Metropolis-Hastings MCMC algorithm to explore both parameter and model space simultaneously, producing posterior probabilities for competing models and enabling Bayes factor estimation without requiring closed-form marginal likelihoods. The canonical extension — reversible-jump MCMC by Green (1995) — handles models of different dimensionalities within a single sampler.	Sequential Monte Carlo (SMC) is a family of simulation-based algorithms that approximate evolving probability distributions by propagating and reweighting a cloud of weighted random draws called particles. It handles nonlinear, non-Gaussian models and streams of data naturally, making it the method of choice for real-time state estimation and posterior approximation over complex distributions.