We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realization.

This forms the basis of our Data Augmented MCMC, which consists of augmenting parameter space with the unobserved PRM value. The resulting simple Metropolis–Hastings sampler acts as an efficient simulation-based inference method, that can easily be transferred from model to model.

Compared with a recent Data Augmentation method based on Gibbs sampling of individual infection histories, PRM-augmented MCMC scales much better with epidemic size and is far more flexible. It is also found to be competitive with Particle MCMC for moderate epidemics when using approximate simulations.

PRM-augmented MCMC also yields a posteriori estimates of the PRM, that represent process stochasticity, and which can be used to validate the model. A pattern of deviation from the PRM prior distribution will indicate that the model underfits the data and help to understand the cause. We illustrate this by fitting a non-seasonal model to some simulated seasonal case count data.

Applied to the Zika epidemic of 2013 in French Polynesia, our approach shows that a simple SEIR model cannot correctly reproduce both the initial sharp increase in the number of cases as well as the final proportion of seropositive.

PRM augmentation thus provides a coherent story for Stochastic Epidemic Model inference, where explicitly inferring process stochasticity helps with model validation.

We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realization.

This forms the basis of our Data Augmented MCMC, which consists of augmenting parameter space with the unobserved PRM value. The resulting simple Metropolis–Hastings sampler acts as an efficient simulation-based inference method, that can easily be transferred from model to model.

Compared with a recent Data Augmentation method based on Gibbs sampling of individual infection histories, PRM-augmented MCMC scales much better with epidemic size and is far more flexible. It is also found to be competitive with Particle MCMC for moderate epidemics when using approximate simulations.

PRM-augmented MCMC also yields a posteriori estimates of the PRM, that represent process stochasticity, and which can be used to validate the model. A pattern of deviation from the PRM prior distribution will indicate that the model underfits the data and help to understand the cause. We illustrate this by fitting a non-seasonal model to some simulated seasonal case count data.

应用于 2013 年法属波利尼西亚的寨卡流行病，我们的方法表明，简单的 SEIR 模型无法正确再现病例数的初始急剧增加以及血清阳性的最终比例。

因此，PRM 增强为随机流行病模型推断提供了一个连贯的故事，其中明确推断过程随机性有助于模型验证。