Statistical Methodology for Multiple Events in Time and Space

我的研究可以分为四个方面。 1.事件发生时间数据，2.动物的相对丰度和分布; 3.语篇分析，4.计数带有多余零的数据。1.今天，我们几乎不间断地收集重症监护室的患者、精准农业中的植物以及参与保险监督计划的司机等的大量数据，目的可以是监测患者的不良事件，确定树木和农业植物的最佳浇水方案，根据司机的驾驶模式为他们设定保险费率。 随着数据收集频率的增加，我们有机会仔细建模解释变量的影响。 我的工作将开发新的模型，解释变量的影响，随着时间的推移而变化的风险和成本的事件，并调查干预的最佳时机。在其他情况下，我们无法持续监测。例如，考虑疾病如癌症的进展。 一种方法是使用多状态模型，其中状态表示癌症的阶段。 我们并不确切知道从第1阶段进展到第2阶段是什么时候发生的，但只在间歇性监测时间有信息，因此在干预时间点可能会出现错误分类。监测时间可以提供关于进展的信息，因为患者可以在感觉不适时预约。 我的工作将开发新的多状态模型与错误分类，允许新的分布，家庭中的个人集群，信息监测时间和辍学。这项工作是至关重要的，因为更好的疾病史建模将使患者得到更好的治疗。2.物种分布的统计模型通常一次只关注一个物种。我建议开发新的多物种模型，利用物种之间的相关性和相互作用，以获得更好的分布估计，并开发方法，随着时间的推移和重要的解释变量的同时选择大量的候选人建模的变化。准确地模拟物种对于保护和面对气候变化至关重要。 目前存在将语料库（文本主体）分类为若干组之一的方法。然而，用于检验组间统计差异的方法还不完善。我将开发测试单词频率之间差异的方法。这是具有挑战性的，因为大量的候选词。4.过零计数模型。计数数据无处不在，包括两周内的癫痫发作次数、交通中的未遂次数等。有时，数据会超过常见模型（如泊松和负二项分布）预测的零。 我将开发新的伽玛和威布尔到达间隔时间与多余的零模型。

My proposed research can be divided into 4 areas. 1. Time-to-Event Data,2. Relative Abundance and Distribution of Animals,3. Text Analysis,4. Count Data with Excess Zeros.1. Today we collect masses of data almost continuously on patients in intensive care units, plants in precision agriculture, and drivers participating in insurance surveillance programs, etc. The purpose can be to monitor patients for adverse events, to determine optimal watering regimes for trees and agricultural plants, to set insurance rates for drivers based on their driving patterns. As the frequency of data collection increases, we have the opportunity to carefully model the effects of explanatory variables. My work will develop novel models for the effects of explanatory variables that change over time on the risk and cost of an event and investigate optimal timing of interventions. In other situations, we are unable to monitor continuously. For instance consider progression of a disease such as cancer. One approach is to use multi-state models with states representing stages of cancer. We do not know exactly when the progression from stage 1 to stage 2 occurred, but have information only at intermittent monitoring times, so that misclassification at intervening time points is likely. The monitoring times may be informative about progression, as patients may make an appointment when feeling unwell. My work will develop novel multi-state models with misclassification, which allow for new distributions, clustering of individuals in families, and informative monitoring times and dropout. This work is critical as better modelling of disease history will allow better treatment of patients. 2. Statistical models for species distributions typically focus on one species at a time. I propose to develop novel multiple-species models, which exploit the correlation and interaction between species to get better estimates of distributions, and to develop methods for modelling changes over time and simultaneous selection of important explanatory variables from a large number of candidates. Modelling species accurately is important for conservation and crucial in the face of climate change.3. Methods currently exist for classification of corpora (bodies of text) into one of several groups. However methods for testing for statistical differences between groups are not well-developed. I will develop methods for testing for differences between word frequencies. This is challenging because of the large number of candidate words. 4. Excess-zero count models. Data on counts are ubiquitous, including number of seizures in a two week period, number of near-misses in traffic, etc. Sometimes the data have an excess of zeros over that predicted by common models such as the Poisson and Negative Binomial. I will develop novel models for gamma and Weibull interarrival times with excess zeros.