On Gibbs Sampling for State Space Models
本文展示了如何用吉布斯采样器对误差为混合正态分布且系数可随时间切换的线性状态空间模型进行贝叶斯推断，通过同时生成整个状态向量和指示变量，并用卡尔曼滤波高效生成状态，实证表明该方法优于逐个生成状态的吉布斯采样器。
We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our approach by several examples and empirically compare its performance to another Gibbs sampler where the states are generated one at a time. The empirical results suggest that our approach is both practical to implement and dominates the Gibbs sampler that generates the states one at a time.