论文标题
使用具有指数衰减的协方差结构的时间序列模型分析计数数据
Analyzing count data using a time series model with an exponentially decaying covariance structure
论文作者
论文摘要
计数数据出现在各种学科中。在这项工作中，已经提出了一种分析时间序列计数数据的新方法。该方法假设在Poisson回归模型中，对于潜在变量，该方法是指数衰减的协方差结构，这是Matérn协方差函数的特殊类别。它是在吉布斯采样和武器抽样技术的帮助下在贝叶斯框架中实施的。提出的方法为协变量效应提供了可靠的估计，并估计了由时间依赖过程和白噪声过程解释的变异性程度。该方法是灵活的，允许不规则的间隔数据，并且可以自然扩展到较大的数据集。贝叶斯实施有助于我们计算后验预测分布，因此对于计数数据预测问题更合适和有吸引力。本文中包含了两种不同口味的现实生活应用。这两个示例和简短的仿真研究表明，所提出的方法具有良好的推论和预测能力，并且比其他竞争模型更好。
Count data appears in various disciplines. In this work, a new method to analyze time series count data has been proposed. The method assumes exponentially decaying covariance structure, a special class of the Matérn covariance function, for the latent variable in a Poisson regression model. It is implemented in a Bayesian framework, with the help of Gibbs sampling and ARMS sampling techniques. The proposed approach provides reliable estimates for the covariate effects and estimates the extent of variability explained by the temporally dependent process and the white noise process. The method is flexible, allows irregular spaced data, and can be extended naturally to bigger datasets. The Bayesian implementation helps us to compute the posterior predictive distribution and hence is more appropriate and attractive for count data forecasting problems. Two real life applications of different flavors are included in the paper. These two examples and a short simulation study establish that the proposed approach has good inferential and predictive abilities and performs better than the other competing models.
