Grant: Discovery Launch Supplement

Data in modern statistical practice is often complex and high-dimensional, necessitating the development of novel and efficient methodology for its analysis. The present proposal is motivated by practical problems arising in disciplines where such data is routinely encountered, such as macro- and microeconomics, finance, biology, and the environment. Over the next five years, my students and I aim to contribute to the development of methodology in four areas. First, high-dimensional Bayesian regression, encountered in applications ranging from finance to biology. Here, the aim is to contribute novel methods for inference in cases where the responses have a group structure. This can occur, for example, when we are predicting the returns of a collection of equities. Second, Bayesian inference for streaming data. This is a key component of designing systems that are able to adapt to new data as it is observed and includes, for example, recommender systems that are able to adapt to the preferences of users. Third, the detection of lead-lag relationships in high-dimensional time series. Lead-lag relationships occur when two time series have similar dynamics with a time delay and can facilitate forecasting tasks in areas such as climate science. Fourth, the clustering of directed graphs. Directed graphs are a powerful way of representing pairwise interaction data, such as transactions between different accounts and migration flows, and can be used to discover structure in such data. The outputs of each objective will include open-source implementations of the novel methods. A thread that runs throughout all four objectives is performing uncertainty quantification via the use of Bayesian methodologies. This makes the proposed methods better suited for applications where accounting for uncertainty is an important component of decision making. In all, my program of research will help train future statisticians to use complex data to make informed decisions about socioeconomic and environmental issues that matter to Canadians.