Prediction for Multi-factor Point Process Models

多因素点过程模型的预测

• 批准号: 0405716
• 负责人: Lawrence Brown
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405716&HistoricalAwards=false
• 关键词: Prediction; Multi; factor; Point; Process

AbstractPI: Lawrence D. BrownProposal: 0405716 This proposal develops two different classes of models for statistical analysis of temporal point processes with covariates. The temporal structure here has a two way character, since there is day-to-day variation and also intraday variation, and these two types of variation must be modeled separately before being combined. Of interest are accurate predictions and also prediction confidence intervals for future observations of the process. One class of models begins by taking a slightly modified square root of the binned point-process counts and then treats these via variations of customary non-linear Gaussian random-effects models. The second class of models begins from a more primitive perspective by developing new classes of point processes having certain properties related to the usual Gaussian paradigm involving Moving Average and Auto Regressive constructions. These point processes are actually special cases of a more general new construction yielding processes with infinitely divisible finite dimensional marginals, and that are analogs in appropriate senses of classical AR and MA Gaussian processes. This new class of models is being adapted and applied to various straightforward temporal settings. The investigators are also studying how to apply such models in the complex settings mentioned above involving covariates and different temporal dimensions. A further area of study is the examination of the differences between the results of analyses involving the new class of stochastic processes and those using the simpler, but approximate, square root idea. Telephone Call Centers are an important and growing component of our modern service-based economy. Proper management of such a center requires estimation of several operational "primitives", combined with queuing theory considerations, in order to determine appropriate staffing levels for efficient and economic customer service. Accurate prediction of the level of customer arrivals is the most difficult of the primitives to assess. Predictions as well as confidence bounds for these predictions are needed. In this proposal two new classes of statistical models particularly attuned to special features of this type of data are developed to make such predictions and confidence statements. While these models are particularly tuned to produce the desired result in the telephone context, they are also adaptable to a wide variety of other prediction problems, particularly to an important class of problems in spatial analysis. In addition, variations of the models are useful in developing techniques for internet intrusion detection. Computer intrusion (attacks by hackers) is an increasing impediment to efficient internet communications, and its detection is one vital step in eliminating this burden.

摘要PI：Lawrence D. BrownProposal：0405716该提案开发了两类不同的模型，用于对具有协变量的时间点过程进行统计分析。这里的时间结构具有双向特征，因为存在日间变化和日内变化，并且这两种类型的变化必须在组合之前单独建模。感兴趣的是准确的预测和预测的置信区间，为未来的观察过程。一类模型首先对分箱的点过程计数取一个稍微修改的平方根，然后通过常规的非线性高斯随机效应模型的变化来处理这些。第二类模型从一个更原始的角度开始，通过开发新的点过程类，这些点过程具有与通常的高斯范式相关的某些属性，包括移动平均和自回归构造。这些点过程实际上是一个更一般的新构造的特殊情况，产生具有无限可分有限维边缘的过程，并且是经典AR和MA高斯过程的适当意义上的类似物。这类新的模型正在适应和应用于各种简单的时间设置。研究人员还在研究如何在上述涉及协变量和不同时间维度的复杂环境中应用此类模型。研究的另一个领域是检查涉及新的一类随机过程和那些使用简单的，但近似的，平方根的想法的分析结果之间的差异。 电话呼叫中心是我们现代服务型经济的一个重要和不断增长的组成部分。这样一个中心的适当管理需要估计几个操作“原语”，结合排队论的考虑，以确定适当的人员配备水平，有效和经济的客户服务。准确预测客户到达的水平是最难评估的基本要素。需要预测以及这些预测的置信界限。在这个建议中，两个新的统计模型，特别是调谐到这种类型的数据的特殊功能，使这样的预测和信心的声明。虽然这些模型是特别调整，以产生所需的结果，在电话的上下文中，他们也适用于各种各样的其他预测问题，特别是一类重要的问题，在空间分析。此外，模型的变化是有用的，在开发技术的互联网入侵检测。计算机入侵（黑客攻击）是有效互联网通信的一个日益严重的障碍，检测它是消除这种负担的一个重要步骤。