Prediction for Multi-factor Point Process Models

摘要本文提出了两种不同的模型，用于具有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，因为存在日变化和日内变化，这两种类型的变化必须在组合之前分别建模。我们感兴趣的是对这一过程的准确预测和未来观测的预测置信区间。一类模型首先对分箱点过程计数进行稍微修改的平方根，然后通过习惯的非线性高斯随机效应模型的变体来处理这些计数。第二类模型从更原始的角度出发，通过开发具有与通常的高斯范式相关的某些属性的新类点过程，包括移动平均和自动回归结构。这些点过程实际上是一种更一般的新结构的特殊情况，产生具有无限可分的有限维边际的过程，并且在适当的意义上类似于经典的AR和MA高斯过程。这类新模型正被适应并应用于各种简单的时间设置。研究人员也在研究如何在上述涉及协变量和不同时间维度的复杂设置中应用这些模型。进一步的研究领域是检查涉及新一类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。对这样一个中心的适当管理需要对几个操作“原语”进行估计，并结合排队理论的考虑，以便确定适当的人员配备水平，以实现高效和经济的客户服务。准确预测顾客到达的水平是最难以评估的原语。我们需要预测以及这些预测的置信范围。在这个建议中，开发了两类新的统计模型，特别适应这类数据的特殊特征，以做出这样的预测和信心声明。虽然这些模型特别适合于在电话环境中产生期望的结果，但它们也适用于各种各样的其他预测问题，特别是空间分析中的一类重要问题。此外，这些模型的变体对开发互联网入侵检测技术也很有用。计算机入侵（黑客攻击）日益阻碍有效的互联网通信，对其进行检测是消除这一负担的关键一步。

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.