Statistical Methodology for Multiple Events in Time and Space

我提出的研究可以分为4个方面。1. 比较数据,2。2 .动物的相对丰度与分布；文本分析4。计数有多余零的数据今天，我们几乎不间断地收集大量数据，包括重症监护病房的病人、精准农业的工厂、参与保险监督计划的司机等。目的可以是监测病人的不良事件，确定树木和农业植物的最佳浇水制度，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，我们有机会仔细模拟解释变量的影响。我的工作将开发新的模型，用于解释变量随时间变化对事件风险和成本的影响，并研究干预的最佳时机。在其他情况下，我们无法持续监控。例如，考虑癌症等疾病的进展。一种方法是使用多状态模型，其中的状态代表癌症的各个阶段。我们不知道从1期进展到2期的确切时间，但只有间歇性监测时间的信息，因此在干预时间点可能会出现错误分类。监测时间可以提供病情进展的信息，因为患者在感觉不适时可以预约。我的工作将开发具有错误分类的新型多状态模型，它允许新的分布，家庭中个体的聚类，以及信息监测时间和辍学。这项工作至关重要，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来更好地估计分布，并开发随时间变化的建模方法，并同时从大量候选变量中选择重要的解释变量。准确地建立物种模型对物种保护非常重要，在气候变化面前也至关重要。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，检验群体间统计差异的方法还没有得到很好的发展。我将开发测试词频差异的方法。这很有挑战性，因为有大量的候选单词。4. 过零计数模型。计数数据无处不在，包括两周内的缉获次数，交通中险些发生的次数等。有时数据比泊松和负二项等常用模型预测的数据有超过零的情况。我将开发具有多余零的伽马和威布尔到达间隔时间的新模型。

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.