Methoden vergleichen

	MCMC für Zeitreihen	Kalman Filter
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1994–1997	1960
Urheber	Carter & Kohn; West & Harrison	Rudolf E. Kalman
Typ	Bayesian posterior sampling for time-ordered data	recursive Bayesian filter
Wegweisende Quelle	Carter, C. K. & Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika, 81(3), 541–553.	Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.
Aliasnamen	MCMC time series, Bayesian time series MCMC, time series posterior sampling, sequential Bayesian MCMC	linear quadratic estimator, LQE, Kalman-Bucy filter, optimal recursive filter
Verwandt	6	5
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 Kalman filter is an optimal recursive algorithm for estimating the hidden state of a linear dynamical system from noisy measurements. At each time step it alternates between a prediction step — projecting the state forward using the system model — and an update step that corrects the prediction with the new observation, producing minimum-variance state estimates and their uncertainty in real time.