System Information Sciences

Statistical Mathematics B03

  • Prof. Yuko Araki  
Keywordsstatistical science, data science, functional data analysis, biostatistics, information criterion, multivariate analysis, high-dimensional data, multi-level model, machine learning

Statistical Mathematics –Theory and application of statistical science –

Statistical mathematics is an indispensable discipline for society. Researchers in the field develop methods and conduct applied research to effectively extract useful information and patterns from data by using mathematics, the common language of science, to deal with the uncertainties in data. 
 
Statistical Modeling 
To extract useful information from high-dimensional data with complicated structure while minimizing loss of information, we develop new statistical models, such as the combination of regularized nonparametric regression models and nonlinear/sparse multivariate analyses.
 
Functional data analysis 
With the rapid development of modern measurement technologies, data are becoming increasingly diverse and complex. Functional data analysis deals with such data, especially that involving functions, shapes,and images. Our research interests consist of building statistical models via regularization, sparse estimation, basis expansions, nonlinear multivariate analysis, Bayesian methods, information criteria,etc. for functional data.
  • Composite basis functions (Araki et al. 2019): Basis functions with sparse singular value decomposition

  • 75th quantile curves estimated by the Bayesian nonparametric quantile mixed-effects models (Tanabe, Araki et al. 2022)