Andrieu, Doucet and Holenstein: particle Markov chain Monte Carlo methods

What changed

Particle 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?

Scientific scope

Particle 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? 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.

Evidence

The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. 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.

Contributors

• The named authors in the research record · SCIENCE: Source-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.

• Wiley full text for particle Markov chain Monte Carlo methods
• Oxford author-hosted particle MCMC manuscript

Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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