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：Lawrence D. BrownProposal：0405716该建议开发了两种不同类别的模型，用于用协变量对时间点过程进行统计分析。此处的时间结构具有两种方式的特征，因为存在日常变化和日内变化，并且在合并之前必须单独对这两种变化进行建模。感兴趣的是准确的预测，也是对未来观察过程的预测置信区间。一类模型首先采用binned点过程计数的稍微修改的平方根，然后通过习惯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，通过开发具有与通常的高斯范式相关的某些属性的新类过程，涉及移动平均值和自动回归构造。这些点过程实际上是一个更通用的新建筑产生过程的特殊情况，具有无限分开的有限维度边缘，并且是对经典AR和Ma Gaussian过程的适当感知的类似物。这种新的模型正在调整并应用于各种直接的时间设置。研究人员还研究了如何在上面提到的协变量和不同时间维度的复杂环境中应用此类模型。研究领域的另一个领域是研究涉及新类随机过程的分析结果与使用更简单但近似平方根的想法的分析结果之间的差异。 电话通话中心是我们现代基于服务的经济的重要组成部分。正确管理此类中心需要估算几种操作“原始人”，并结合排队理论的注意事项，以确定适当的人员配备水平以进行高效和经济客户服务。准确预测客户到达水平是原始人中最困难的评估。需要对这些预测的预测和置信界。在此提案中，开发了两种新的统计模型，特别适合此类数据的特殊特征，以做出此类预测和信心陈述。尽管这些模型在电话环境中尤其调整为产生所需的结果，但它们也适合各种其他预测问题，尤其是在空间分析中的重要类别。此外，模型的变化对于开发用于Internet入侵检测的技术很有用。计算机入侵（黑客攻击）是对有效的Internet通信的越来越多的障碍，并且其检测是消除这一负担的重要一步。