论文标题
通过共享参数耦合的多个状态空间模型的边缘化粒子吉布斯
Marginalized particle Gibbs for multiple state-space models coupled through shared parameters
论文作者
论文摘要
我们考虑了由公共状态空间模型（SSM）结构描述的多个时间序列中的贝叶斯推断，但在不同的子模型之间共享不同的参数子集。一个重要的例子是疾病动力学，其中参数可以是疾病或特定于位置的。这些模型中的参数推断可以通过系统地汇总不同时间序列的信息来改进，最著名的是短序列。粒子吉布斯（PG）采样器是一种有效的SSM中推断算法类别，特别是当可以利用共轭以从状态更新中分离模型参数时。我们提出了两个不同的PG采样器，它们可以将静态模型参数边缘化：一个在数据集中在数据集中更新一个模型的另一个模型，而另一个模型则通过将所有模型堆叠到高维SSM中，同时更新所有模型。每个采样器的独特特征使它们适合不同的建模环境。我们提供有关何时应该使用每个采样器的见解，并证明它们可以组合起来形成一个有效的PG采样器，用于在状态和参数之间具有很强依赖性的模型。在两个线性高斯示例和关于蚊子传播疾病传播的现实示例上进行了表现。
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.
