# Particle Gibbs with Ancestor Sampling

arXiv: https://arxiv.org/abs/1401.0604 · HTML: https://mlsanity.com/paper/1401.0604/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2014.

## Built on by (most cited first, 21 of 21)

- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)
- [Variational Gaussian Process Diffusion Processes](https://mlsanity.com/paper/2306.02066/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Learning-to-Defer in Non-Stationary Time Series via Switching State-Space Models](https://mlsanity.com/paper/2601.22538/) (2026)
- [State and parameter learning with PaRIS particle Gibbs](https://mlsanity.com/paper/2301.00900/) (2023)
- [Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design](https://mlsanity.com/paper/2409.05354/) (2024)
- [De-Sequentialized Monte Carlo: a parallel-in-time particle smoother](https://mlsanity.com/paper/2202.02264/) (2022)
- [STEADY: Simultaneous State Estimation and Dynamics Learning from Indirect Observations](https://mlsanity.com/paper/2203.01299/) (2022)
- [PyDPF: A Python Package for Differentiable Particle Filtering](https://mlsanity.com/paper/2510.25693/) (2025)
- [Statistical Distance Based Deterministic Offspring Selection in SMC Methods](https://mlsanity.com/paper/2212.12290/) (2022)
- [Bayesian Learning in a Nonlinear Multiscale State-Space Model](https://mlsanity.com/paper/2408.06425/) (2024)
- [Bayesian Inference and Learning in Nonlinear Dynamical Systems: A Framework for Incorporating Explicit and Implicit Prior Knowledge](https://mlsanity.com/paper/2508.15345/) (2025)
- [Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes](https://mlsanity.com/paper/2511.05330/) (2025)
- [Marginalized particle Gibbs for multiple state-space models coupled through shared parameters](https://mlsanity.com/paper/2210.07379/) (2022)
- [Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systems](https://mlsanity.com/paper/2303.00301/) (2023)
- [Learning to Approximate Particle Smoothing Trajectories via Diffusion Generative Models](https://mlsanity.com/paper/2406.00561/) (2024)
- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)
- [State-Coupled Volatility in Latent Dynamical Systems: Recovery Under Partial Observation](https://mlsanity.com/paper/2606.02664/) (2026)
- [Nonlinear Bayesian Estimator for Parameter Learning: A Fixed-Point Characterization](https://mlsanity.com/paper/2606.10111/) (2026)

## Abstract (arXiv)

Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models.