Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Non-centred Bayesian inference for discrete-valued state-transition models: the Rippler algorithm

James Neill, Lloyd A. C. Chapman, Chris Jewell

TL;DR

The paper tackles inference in discrete-valued, high-dimensional epidemic state-transition models by framing the problem as a coupled hidden Markov model and proposing a novel non-centered data-augmentation MCMC algorithm, the Rippler method, to jointly infer latent states and parameters. Rippler perturbs a latent uniform matrix $U$ to generate proposed latent states $X^*$, moving computations of event probabilities into the proposal step and accepting via Metropolis-Hastings. A data-informed extension uses observations to shape proposals and normalizing constants, improving mixing in complex models; Rippler scales linearly with the number of states $S$, outperforming RJMCMC and iFFBS as $S$ grows. Simulations across SIR, SEIR, and multi-strain models show improved latent-space exploration and scalability, with open-source Python code provided for reproducibility.

Abstract

Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference on individuals' unobserved disease statuses over time, which form a high-dimensional and highly correlated state space. We introduce a novel Bayesian (data-augmentation Markov chain Monte Carlo) algorithm for jointly estimating the model parameters and unobserved disease statuses, which we call the Rippler algorithm. This is a non-centred method that can be applied to any individual-based state-transition model. We compare the Rippler algorithm to the state-of-the-art inference methods for individual-based stochastic epidemic models and find that it performs better than these methods as the number of disease states in the model increases.

Non-centred Bayesian inference for discrete-valued state-transition models: the Rippler algorithm

TL;DR

The paper tackles inference in discrete-valued, high-dimensional epidemic state-transition models by framing the problem as a coupled hidden Markov model and proposing a novel non-centered data-augmentation MCMC algorithm, the Rippler method, to jointly infer latent states and parameters. Rippler perturbs a latent uniform matrix to generate proposed latent states , moving computations of event probabilities into the proposal step and accepting via Metropolis-Hastings. A data-informed extension uses observations to shape proposals and normalizing constants, improving mixing in complex models; Rippler scales linearly with the number of states , outperforming RJMCMC and iFFBS as grows. Simulations across SIR, SEIR, and multi-strain models show improved latent-space exploration and scalability, with open-source Python code provided for reproducibility.

Abstract

Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference on individuals' unobserved disease statuses over time, which form a high-dimensional and highly correlated state space. We introduce a novel Bayesian (data-augmentation Markov chain Monte Carlo) algorithm for jointly estimating the model parameters and unobserved disease statuses, which we call the Rippler algorithm. This is a non-centred method that can be applied to any individual-based state-transition model. We compare the Rippler algorithm to the state-of-the-art inference methods for individual-based stochastic epidemic models and find that it performs better than these methods as the number of disease states in the model increases.
Paper Structure (30 sections, 3 theorems, 41 equations, 15 figures, 2 algorithms)

This paper contains 30 sections, 3 theorems, 41 equations, 15 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Epidemic Modelling
  3. Coupled Hidden Markov Models
  4. Transition Probabilities for Epidemics
  5. Simulation and Non-centering
  6. Bayesian Inference: The Rippler Algorithm
  7. Overview
  8. Proposal Mechanism
  9. Acceptance Probability
  10. Adaptive Tuning
  11. Summary
  12. Data-informed Rippler Algorithm
  13. Bayesian Inference: Existing Methods
  14. Existing Inference Methods
  15. Computational Complexity Comparison
  16. ...and 15 more sections

Key Result

Proposition 1

We have $\pi(\boldsymbol{X}|\boldsymbol{\theta})q_1(\boldsymbol{U}|\boldsymbol{\theta},\boldsymbol{X}) = 1$ and $\pi(\boldsymbol{X}^{\ast}|\boldsymbol{\theta})q_1(\boldsymbol{U}^{\ast}|\boldsymbol{\theta},\boldsymbol{X}^{\ast}) = 1$.

Figures (15)

  • Figure 1: Visualisation of a coupled hidden Markov model with $\mathcal{N} =3$ (from $t=1$ to $t=4$). Note that only a subset of time-individual points have observations. Based on a figure from touloupou2020scalable.
  • Figure 2: Visualisation of the SIR model (where $\beta$ is the infection rate, $\gamma$ is the recovery rate, and $I(t)$ is the current number of infective individuals).
  • Figure 3: Posterior samples of the number of individuals in each state over time, using the Rippler (top left), data-informed Rippler (top right), reversible-jump (bottom left), and iFFBS (bottom right) methods on the SIR model. The median values are shown in the solid lines and the 95% credible intervals are shown in the shaded regions. The true values are shown by the dashed lines.
  • Figure 4: Visualisation of the SEIR model with $\mathcal{S}_E=3$ exposure steps.
  • Figure 5: Relative time taken (left) and MAJD per relative unit time (right) for hidden state inference methods on the extended exposure model (from $\mathcal{S}=4$ to $\mathcal{S}=10$).
  • ...and 10 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Proposition 2
  • Proposition 3