# Marginalized particle Gibbs for multiple state-space models coupled through shared parameters

arXiv: https://arxiv.org/abs/2210.07379 · HTML: https://mlsanity.com/paper/2210.07379/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [An Introduction to Probabilistic Programming](https://mlsanity.com/paper/1809.10756/) (2018)
- [Particle Gibbs with Ancestor Sampling](https://mlsanity.com/paper/1401.0604/) (2014)
- [Automated learning with a probabilistic programming language: Birch](https://mlsanity.com/paper/1810.01539/) (2018)
- [Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs](https://mlsanity.com/paper/1708.07787/) (2017)
- [Functional Tensors for Probabilistic Programming](https://mlsanity.com/paper/1910.10775/) (2019)
- [Parameter elimination in particle Gibbs sampling](https://mlsanity.com/paper/1910.14145/) (2019)
- [A framework for studying synaptic plasticity with neural spike train data](https://mlsanity.com/paper/1411.4077/) (2014)
- [Autoconj: Recognizing and Exploiting Conjugacy Without a Domain-Specific Language](https://mlsanity.com/paper/1811.11926/) (2018)
- [Particle Gibbs with Ancestor Sampling for Probabilistic Programs](https://mlsanity.com/paper/1501.06769/) (2015)
- [Efficient sequential Monte Carlo algorithms for integrated population models](https://mlsanity.com/paper/1708.04221/) (2017)

## Abstract (arXiv)

We consider Bayesian inference from multiple time series described by a common state-space model (SSM) structure, but where different subsets of parameters are shared between different submodels. An important example is disease-dynamics, where parameters can be either disease or location specific. Parameter inference in these models can be improved by systematically aggregating information from the different time series, most notably for short series. Particle Gibbs (PG) samplers are an efficient class of algorithms for inference in SSMs, in particular when conjugacy can be exploited to marginalize out model parameters from the state update. We present two different PG samplers that marginalize static model parameters on-the-fly: one that updates one model at a time conditioned on the datasets for the other models, and one that concurrently updates all models by stacking them into a high-dimensional SSM. The distinctive features of each sampler make them suitable for different modelling contexts. We provide insights on when each sampler should be used and show that they can be combined to form an efficient PG sampler for a model with strong dependencies between states and parameters. The performance is illustrated on two linear-Gaussian examples and on a real-world example on the spread of mosquito-borne diseases.