Many quantities characterizing infectious disease outbreaks - like the effective reproduction number ($R_t$), defined as the average number of secondary infections a newly infected individual will cause over the course of their infection - need to be modeled as time-varying parameters. It is common practice to use Gaussian random walks as priors for estimating such functions in Bayesian analyses of pathogen surveillance data. In this setting, however, the random walk prior may be too permissive, as it fails to capture prior scientific knowledge about the estimand and results in high posterior variance. We propose several Gaussian Markov process priors for $R_t$ inference, including the Integrated Brownian Motion (IBM), which can be represented as a Markov process when augmented with its corresponding Brownian Motion component, and is therefore computationally efficient and simple to implement and tune. We use simulated outbreak data to compare the performance of these proposed priors with the Gaussian random walk prior and another state-of-the-art Gaussian process prior based on an approximation to a Matérn covariance function. We find that IBM can match or exceed the performance of other priors, and we show that it produces epidemiologically reasonable and precise results when applied to county-level SARS-CoV-2 data.

翻译：传染病暴发的许多特征量——如有效再生数（$R_t$），定义为新感染个体在其感染周期内平均导致的继发感染数——需要建模为时变参数。在病原体监测数据的贝叶斯分析中，通常使用高斯随机游走作为估计此类函数的先验。然而在此背景下，随机游走先验可能过于宽松，因其未能纳入关于估计量的先验科学知识，并导致较高的后验方差。我们提出了几种用于$R_t$推断的高斯马尔可夫过程先验，包括积分布朗运动（IBM）。当与其对应的布朗运动分量结合时，IBM可表示为马尔可夫过程，因而计算高效且易于实现与调参。我们使用模拟暴发数据比较了这些提议先验与高斯随机游走先验，以及另一种基于Matérn协方差函数近似的最先进高斯过程先验的性能。研究发现IBM能够匹配或超越其他先验的性能，并在应用于县级SARS-CoV-2数据时产生符合流行病学预期且精确的结果。