विधियों की तुलना करें
चुनी हुई विधियों की आमने-सामने समीक्षा करें; भिन्नता वाली पंक्तियाँ रेखांकित हैं।
| माप त्रुटि के साथ अनुक्रमिक मोंटे कार्लो× | मार्कोव चेन मोंटे कार्लो (MCMC)× | |
|---|---|---|
| क्षेत्र≠ | बायेसियन | अनुकरण |
| परिवार≠ | Bayesian methods | Process / pipeline |
| उद्भव वर्ष≠ | 1993–2001 | 1953 (Metropolis-Hastings); 1984 (Gibbs) |
| प्रवर्तक≠ | Gordon, Salmond & Smith (1993); extended by Doucet, de Freitas & Gordon (2001) | Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984) |
| प्रकार≠ | Sequential Bayesian filtering | Simulation-based Bayesian inference / numerical integration |
| मौलिक स्रोत≠ | Doucet, A., de Freitas, N., & Gordon, N. (Eds.). (2001). Sequential Monte Carlo Methods in Practice. Springer New York. ISBN: 978-0-387-95146-1 | Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC. DOI ↗ |
| उपनाम | SMC with measurement error, particle filter with noisy observations, SMC state-space measurement error, sequential particle filtering with observation noise | MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs) |
| संबंधित≠ | 6 | 5 |
| सारांश≠ | Sequential Monte Carlo (SMC) with measurement error is a particle-based Bayesian filtering method for tracking hidden states in dynamical systems when observations are corrupted by noise. It propagates a weighted cloud of particles through time, updating weights at each step to reflect how well each particle explains the noisy measurement, and produces a full posterior distribution over the latent state at every time point. | Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution. |
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