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.

AbstractPI：Lawrence D. Brown 提案：0405716 该提案开发了两类不同的模型，用于协变量的时间点过程的统计分析。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在组合之前必须分别建模。令人感兴趣的是准确的预测以及未来过程观察的预测置信区间。一类模型首先对分箱点过程计数进行稍微修改的平方根，然后通过常规非线性高斯随机效应模型的变体来处理这些模型。第二类模型从更原始的角度开始，通过开发具有与涉及移动平均和自回归构造的常见高斯范式相关的某些属性的新类点过程。这些点过程实际上是具有无限可分的有限维边缘的更一般的新构造产生过程的特例，并且在适当意义上是经典 AR 和 MA 高斯过程的类似物。这类新模型正在被调整并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。进一步的研究领域是检查涉及新型随机过程的分析结果与使用更简单但近似的平方根思想的分析结果之间的差异。 电话呼叫中心是现代服务型经济中一个重要且不断增长的组成部分。对这样一个中心的正确管理需要对几个操作“原语”进行估计，并结合排队论考虑因素，以便确定适当的人员配备水平，以提供高效且经济的客户服务。准确预测顾客到达水平是最难评估的基元。需要预测以及这些预测的置信界限。在该提案中，开发了两类新的统计模型，特别适合此类数据的特殊特征，以做出此类预测和置信度陈述。虽然这些模型经过专门调整以在电话环境中产生所需的结果，但它们也适用于各种其他预测问题，特别是空间分析中的一类重要问题。此外，模型的变体对于开发互联网入侵检测技术很有用。计算机入侵（黑客攻击）日益成为高效互联网通信的障碍，其检测是消除这一负担的重要一步。