Statistical Methodology for Multiple Events in Time and Space

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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.**