Links Between Parametric and Nonparametric Methods

Professor Mayer Alvo in front of a black board with formulas written on it in white chalk

Dr. Mayer Alvo with colleagues Hang Xu (PhD candidate) and Professor Philip Yu from the University of Hong Kong

Department of Mathematics and Statistics

The work that Dr. Mayer Alvo conducts with his colleagues, Hang Xu and University of Hong Kong professor Philip Yu, focuses on ranking data, the process by which input data is sorted and organized according to rank. An example would be the numbering of data from 1 to n according to value, 1 being the smallest value in the dataset and n being the largest. Data of this sort falls within the realm of nonparametric statistics and is typically very difficult to manage in terms of analysis and calculations. By contrast, sample data that can be characterized by a known distribution except for some fixed parameters is generally analyzed by the more powerful methods developed in parametric statistics.

In a recent paper, Alvo discovered a way to bridge the gap between parametric and nonparametric statistical methods of data analysis, to exploit the best aspects of the former while enjoying the robust properties of the latter. He and his colleagues introduced Bayesian methods to ranking data, making it much easier to analyze datasets with many different attributes. This approach can be used in statistical situations ranging from examining how the preference for different types of sushi varies between different geographical regions in Japan to classifying breast cancer patients based on gene expression data. This research is not only important for the mathematical world, but also the medical world. For instance, with the development of more powerful methods for detecting multiple change points, researchers and doctors will be able to extract more information from genetic data and take preventive action earlier.

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