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In statistics, data collection is a difficult process that demands thoughtful consideration. Securing a sufficient sample size can be challenging, or even impossible, regardless of the method employed. Small area estimation is a promising statistical technique that not only focuses on the target data but also incorporates data from related areas to improve mathematical accuracy.
We spoke with Masayo Hirose, a researcher specializing in small area estimation, who shared the unique appeal of this field, the future direction of her work, and the message she hopes to convey to students.

Pursuing accuracy despite insufficient sample sizes

Could you tell us about your research?

I specialize in small area estimation within the field of mathematical statistics. This discipline is essential for building objective, scientific evidence, and it transcends boundaries—from the humanities to the sciences, and even into medicine. While many statistical methods are already in use across various applied fields, I believe there is still significant room for innovation and advancement.

What exactly is small area estimation?

Imagine trying to estimate the mean not at the national level, but for smaller geographic areas, such as prefectures or municipalities. While the overall sample size might be sufficient, subdividing further could result in an insufficient sample size for certain subgroups or regions. In such cases, small area estimation allows us to incorporate information from neighboring regions to improve statistical accuracy, even if only slightly. Of course, there are limitations, but I believe this methodology still holds great potential. Based on this premise, my research focuses on identifying approaches to enhance precision in addressing real-world challenges. I am particularly interested in exploring the extent to which mathematical methods can contribute to solving these issues.

So, you’re developing new theories?

Yes. My work centers on creating new theoretical models for developing a new estimating method and applying it to data analysis. While my experience with hands-on, real-life data analysis is a little limited compared to applied researchers, I’ve recently begun expanding my focus to examine how these developing methods can be applied to real-world issues.

For example, I’ve looked at data related to employment and labor conditions across Japan. Previous studies often estimated values for each prefecture using only local data within each prefecture. I analyzed to explore how factors vary across prefectures, genders, and age groups. Through this process, I identified potential concerns regarding insufficient sample size in certain areas. This led me to consider the potential of applying small area estimation techniques to Japanese data.

The joy of developing new methods and the challenge of spreading them

What aspects of your current field do you find most appealing?

I’m deeply attracted to the mathematical properties, but what excites me most is the possibility that the methodologies I develop could benefit society. I once saw an area-based map with high statistical precision that clearly highlighted regions requiring attention. That experience helped me understand the importance of making these precise statistical maps. What I find most compelling is the potential for my theoretical works and methods to go beyond academic research and make meaningful contributions to society.

However, bridging the gap between theory and application remains a challenge. Even superior methods often take time to gain acceptance in applied fields. Yet, even after accomplishing this, it does not necessarily mean the method will be applied to practical fields right away. Practical adoption depends on whether the researchers working in applied fields believe that it can be used in the real world, I feel.

Discovering the power of perseverance abroad

Can you share any memorable stories from your research to date?

During the early days of my visit to the University of Maryland, I struggled to communicate effectively. Despite that, I had to proactively generate ideas and present results to build relationships and gain recognition as a visiting student. I remember approaching my mentor and saying, “Would you allow me to discuss this briefly?” Each time, he encouraged me—but also told me, “It’s not sufficient.”

About six months after arriving, my mentor finally said, “This result is quite intriguing. Let’s explore it further.” I still vividly remember how happy I felt when my professor acknowledged my work.

Over time, I built a strong relationship of trust with that professor, which led to nearly a decade of collaborative research. It took a long time to earn that trust, but I never gave up. Having my efforts finally recognized remains one of the most memorable experiences in my research career.

Did you notice any differences in the research environment between the U.S. and Japan?

In the U.S., I noticed that researchers often take a proactive approach to addressing social issues through mathematics. I was impressed by how thoughtfully they applied their research to real-world challenges. My mentor consistently emphasized the importance of conducting research that makes a meaningful impact on society.

One example is the study of our current poverty situation. We can begin to design more thoughtful and effective policy measures by visualizing poverty rates in finer detail. Through my experiences in the U.S., I came to truly appreciate the societal value of mathematical statistics. I hope that, in the future, precise statistical approaches will become a standard tool for addressing social issues in Japan, just as they are in the U.S.

The value gained from understanding the mathematical essence

What do you keep in mind when teaching students?

In my regular classes, I often teach statistics to students from applied fields. I emphasize the importance of understanding the mathematical principles behind the methods, rather than relying solely on software.

Some people believe, “Simply knowing how to use software is enough.” But I don’t share that view. I have no intention of dismissing the value of software. On the contrary, I believe it’s an incredibly powerful tool that should be actively used.

However, it’s ultimately up to the data analyst who decides what data to input and how to interpret the results. The depth of a data analyst’s knowledge and technical skills is fundamental to obtaining high-quality scientific evidence.

So, you’re saying we shouldn’t blindly trust software?

Exactly. Put simply, having even a basic grasp of mathematics allows students to use software more confidently and responsibly. For example, when working on a graduation thesis, students often rely on statistical methods. I encourage them to develop true software literacy—understanding how the software works and how its results are generated.

I believe it’s perfectly fine if students don’t grasp everything immediately. These concepts are difficult, and mastering them takes time and effort. What matters is striving to understand the mathematics behind the tools. I believe that the logical thinking skills cultivated during the process will lead to future growth. If students cultivate the habit of questioning and thinking independently in their daily lives, it will help them navigate real-world challenges with confidence.

Developing methods that help improve society

Could you share your future vision or goals?

Although my research is still ongoing, I hope to eventually develop highly precise methods that can be applied not only in urban areas but also in smaller communities and regions. I hope to contribute to building evidence that can be reflected in policy-making or service planning in Japan.

Lastly, do you have any advice for students who are unsure about their career path?

I would like to convey the message that no matter your gender, you can study mathematics. However, even today, women in Japan are less likely to pursue careers in science or math. At times, female students may feel anxious or isolated when considering a career in these fields. I remember feeling the same uncertainty when I was a student. In the U.S., I encountered many talented female researchers and students who were actively engaged in academia. Globally, it’s common to see female researchers—they’re not considered very unusual.

If you have a path you want to pursue, I encourage you to take the first step. You may worry about failure, but a life without failure is a life without experience—and without experience, there can be no success. Even when you fail, those failures can enrich your life.

Indeed, mathematics is built upon the steady accumulation of experience

Exactly. Mathematics is a discipline of accumulated knowledge. Meaningful research outcomes rarely appear immediately. With patience and persistence, continuous study will eventually lead to the moment when the dots connect, and you see the light—that’s when all the effort is finally rewarded. To me, it’s so captivating and is the true essence of mathematics. I believe it’s the same in life. Even if things don’t blossom immediately, I hope students will keep exploring what they like and what inspires them, without fear of failure.