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        "description": "The three-author 2010 framework, including particle independent Metropolis-Hastings, particle marginal Metropolis-Hastings and particle Gibbs. Target invariance and convergence require their separate support, resampling and ideal-chain assumptions. Particle-Gibbs invariance at N>=1 is not ergodicity at N=1; the convergence theorem requires N>=2. Existing SMC and pseudo-marginal results retain their own credit; no universal fast-mixing guarantee.",
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      "statement": "# Andrieu, Doucet and Holenstein: particle Markov chain Monte Carlo methods\n\nParticle filters approximate hidden states using a finite collection of simulated possibilities. MCMC methods instead build a chain designed to preserve a target distribution. Particle MCMC connects the two by treating the random choices inside a particle filter as part of a larger mathematical state. This allows particle-based proposals to preserve the intended posterior exactly under stated assumptions, even with finitely many particles. Exactness of the stationary target still leaves a practical question: how quickly does the chain explore it?\n\n## Scientific scope\n\nThe three-author 2010 framework, including particle independent Metropolis-Hastings, particle marginal Metropolis-Hastings and particle Gibbs. Target invariance and convergence require their separate support, resampling and ideal-chain assumptions. Particle-Gibbs invariance at N>=1 is not ergodicity at N=1; the convergence theorem requires N>=2. Existing SMC and pseudo-marginal results retain their own credit; no universal fast-mixing guarantee.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nChristophe Andrieu; Arnaud Doucet; Roman Holenstein\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [Wiley full text for particle Markov chain Monte Carlo methods](https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1467-9868.2009.00736.x)\n- [Oxford author-hosted particle MCMC manuscript](https://www.stats.ox.ac.uk/~doucet/andrieu_doucet_holenstein_PMCMC.pdf)\n",
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      "title": "Andrieu, Doucet and Holenstein: particle Markov chain Monte Carlo methods"
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