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Statistical Science and its Applications

Yoshiyuki Ninomiya
Degree: Doctor of Philosophy (The Graduate University for Advanced Studies)
Research Interests: Mathematical statistics
Unit: Space & Flow

Report

In the 21th century, huge and diversified data are accumulated in various scientific and industrial fields owing to advances of computers and measurement technology, and the demand of statistics is increasing to deal with such data. In addition, since the advance of computers not only enable to accumulate huge data but also improve the speed of analysis dramatically, to make a new computational method becomes an important issue in statistics.

Of course, it is totally wrong to say that theories which do not depend on computers have no demand now. For instance, such a theory are used as an important part of computational method. If a theory makes the computational load for a whole analysis 1/100 or 1/1000, it will have a great significance. It is because we can use the cut computational load to do more complicated analysis.

In this way, it is now needed to develop an agreed-upon middle ground between computational method and theoretical method in statistics. Actually, in the NSF report of "Statistics: Challenges and Opportunities for the Twenty-First Century", "Middle ground between proof and computational experiment" is selected as one of six research challenges in the 21th century. In this challenge, a problem for the model with non-identifiability is written as an example. The model with non-identifiability is defined as the model having a point which has several different parametric expressions, and it is depicted as in Figure 1. Owing to the non-identifiability, we need a different statistical theory to treat it.

My research object is the statistical theory for irregular models including the model with non-identifiability. Although the irregular model is defined as the model to which the conventional statistical theory cannot be applied, it is needed in various fields. For instance, the change-point model, the mixture model, hidden Markov model, neural network model or factor analysis model is one of the irregular models and basic model in economics, engineering or psychology.

My most recent research is to derive a theory about a model selection for the factor analysis model from its graphical representation depicted in Figure 2. In fact, this research was started by request from a psychologist. I will do my research and instruction based on this style, that is I will interact with not only mathematical field but also other scientific and industrial fields and treat problems with a large demand from them. In addition, I will foster human resources with both mathematical and applied skill to contribute to "Math-for-Industry".

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