# New Research

2017/06/01

# Mathematical statistics and applications to statistical modeling for stochastic processes

## For the development of big dependent data analysis

### Professor・Masayuki Uchida, Associate professor・Kengo Kamatani, Assistant professor・Yoshikazu Terada

We have mainly been studying (1) statistical inference for stochastic processes, (2) computational statistics and (3) statistical learning theory in our laboratory. In particular, applications to statistical finance, actuarial mathematical statistics, statistical seismology, survival analysis, Bayes statistics with MCMC method, machine learning and fMRI data analysis are very important research fields in mathematical science for social systems.

(1) Statistical inference for stochastic processes

In statistical finance, actuarial mathematical statistics, statistical seismology and survival analysis, continuous time stochastic processes are standard mathematical models and statistical analysis is done based on stochastic differential equation and stochastic analysis. For statistical modeling of stochastic processes, we often use several methods of mathematical statistics, for example, statistical estimation and statistical hypothesis test.

(2) Bayes statistics with MCMC method

We are also working on computational methodologies for dependent data analysis. From the late 1980s, Bayesian methodologies have developed extensively due to Monte Carlo methods. Another methodological revolution is required for the analysis of big dependent data. Scalable Monte Carlo methods for Bayesian big data analysis is one of the main subjects in our laboratory.

(3) Machine learning and fMRI data analysis

Recently, machine learning has drawn much attention. In our laboratory, we focus on the statistical theory of unsupervised learning such as clustering, dimension reduction. Moreover, we develop new methods to analysis the complex data including the brain information data, network data, and functional data and provide theoretical properties of these methods.

Our researches are related to various fields of science and technology such as stochastic analysis, mathematical statistics, computational statistics, statistical learning theory, financial and insurance mathematics and data analysis.