A dynamic approach to the statistical analysis of point processes
A dynamic approach to the statistical analysis of point processes
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点过程统计分析的动态方法
DOI：
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发表时间：
1992
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通讯作者：
D. Gamerman
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文献类型：
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作者：
D. Gamerman
概要提出了一种基于假设分段恒定强度率的连续间隔的顺序分析的点过程分析方法。具有解释变量的过程的贝叶斯推理是通过在线估计、过滤和预测得出的。获得了时间连续强度率的限制方程，并针对无协变量的情况进行了求解。提供了示例，并在数值示例中应用了该方法。类似的方法包括 Koch & Spreij (1983) 和 Snyder (1975, ? 6) 的工作，它们也使用带有系统方程的动态模型。这些基于时间连续过程过滤理论的方法提供了良好的概率描述。他们的主要问题是即使在简单的问题中也很难在存在协变量的情况下应用结果。本文的目的是为带有解释变量的点过程的推理问题提供易于处理且合理的解决方案。 Azzalini (1982) 警告说，即使在没有协变量的情况下，过滤理论所需的精确计算也很复杂。该方法基于并在某种程度上概括了生存数据工作（Gamerman，1991）。推理是根据模型参数的在线和平滑或过滤估计以及基于过去信息对未来发生的预测来考虑的。在 ？ 2、模型陈述和推导程序推导。在 ？ 3、详细考虑没有协变量的模型和任何连续率的限制方程
SUMMARY An approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented. Bayesian inference for processes with explanatory variables is derived in terms of on-line estimation, filtering and prediction. Limiting equations for the time-continuous intensity rate are obtained and solved for the no-covariates case. Examples are provided and the approach is applied in a numerical example. Similar approaches include the work of Koch & Spreij (1983) and Snyder (1975, ? 6) which also use a dynamic model with a system equation. These approaches based on filtering theory for time continuous processes provide good probabilistic descriptions. Their main problem is the difficulty in applying the results in the presence of covariates even in simple problems. The purpose of this paper is to provide tractable yet reasonable solutions to the inference problem of point processes with explanatory variables. Azzalini (1982) warns about the complications of exact calculations required by filtering theory even in the absence of covariates. The approach is based on, and to some extent generalizes, work on survival, data (Gamerman, 1991). Inference is considered in terms of on-line and smoothed or filtered estimation of model parameters and prediction of future occurrences based on past information. In ? 2, the model is stated and inference procedures derived. In ? 3, the model with no covariates is considered in detail and limiting equations for any continuous rate