Posterior Mode Estimation by Extended Kalman Filtering for Multivariate Dynamic Generalized Linear Models
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用扩展卡尔曼滤波估计多变量动态广义线性模型的后验众数
- 研究问题
- 如何对指数族观测的多变量动态模型进行滤波与平滑，尤其处理计数、二元及非平稳多类别时间序列？
- 方法与思路
- 作者以时变参数的后验众数代替完整贝叶斯积分，并推广扩展卡尔曼滤波与平滑，获得近似后验众数估计。
- 材料陈述的贡献
- 摘要称，文章提供多变量动态广义线性模型框架；模拟显示良好的估计表现，并给出多类别商业调查数据应用。
- 阅读关注点
- 应核对状态演化和观测模型、后验众数近似的推导、滤波与平滑误差，以及高维或非平稳情形的表现。
- 阅读边界
- 摘要未提供近似误差界、模拟数值或普遍性能保证，后验众数也不等于完整后验；索引稿件版本与刊本变化未知。
原文摘要
A family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family. Besides common conditionally Gaussian models, this article deals with univariate models for counted and binary data and, as the most interesting multivariate case, models for nonstationary multicategorical time series. For univariate responses, a related yet different class of models has been introduced in a Bayesian setting by West, Harrison and Migon. Assuming conjugate prior-posterior distributions for the natural parameter of the exponential family, they derive an approximate filter for estimation of time-varying states or parameters. However, their method raises some problems; in particular, in extending it to the multivariate case. A different approach to filtering and smoothing is chosen in this article. To avoid a full Bayesian analysis based on numerical integration, which becomes computationally critical for higher dimensions, we propose to estimate time-varying parameters by posterior modes. A generalization of the extended Kalman filter and smoother for conditionally Gaussian observations is suggested for approximate posterior mode estimation. For the purpose of comparison, it is applied to data sets analyzed by the authors mentioned earlier. The quality of approximation is also studied by simulation experiments, indicating good estimation behavior, and an application to multicategorical business test data is given.