Methoden vergleichen

	MCMC für Zeitreihen	Partikelfilter (Sequentieller Monte-Carlo-Algorithmus)
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1994–1997	1993
Urheber	Carter & Kohn; West & Harrison	Gordon, Salmond & Smith
Typ	Bayesian posterior sampling for time-ordered data	Sequential Monte Carlo estimator
Wegweisende Quelle	Carter, C. K. & Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika, 81(3), 541–553.	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	MCMC time series, Bayesian time series MCMC, time series posterior sampling, sequential Bayesian MCMC	SMC, sequential Monte Carlo, bootstrap filter, condensation algorithm
Verwandt	6	4
Zusammenfassung	Time series MCMC applies Markov chain Monte Carlo methods to Bayesian inference over time-ordered data. Rather than optimising a single parameter estimate, it draws samples from the full joint posterior of parameters and latent states, yielding probability distributions that honestly reflect uncertainty about dynamics, trends, and seasonal patterns across every time point.	The particle filter, introduced by Gordon, Salmond, and Smith in 1993, is a sequential Monte Carlo algorithm that approximates the Bayesian filtering distribution for nonlinear and non-Gaussian state-space models. Rather than tracking a single best estimate, it maintains a cloud of N weighted random samples — particles — that collectively represent the full posterior distribution of a hidden state at each point in time as new observations arrive.