手法を比較

	時系列MCMC	ハミルトニアンモンテカルロ
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1994–1997	1987
提唱者	Carter & Kohn; West & Harrison	—
種類	Bayesian posterior sampling for time-ordered data	Gradient-based Markov chain Monte Carlo sampler
原典	Carter, C. K. & Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika, 81(3), 541–553.	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
別名	MCMC time series, Bayesian time series MCMC, time series posterior sampling, sequential Bayesian MCMC	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
関連	6	3
概要	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.	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.