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Statistics doctoral student Andrew Simpson has found great success in the complicated field of large-scale number crunching and data analysis.

He already holds a bachelor’s degree in mathematics and statistics (2021) and a master’s degrees in statistics (2022). In 2026, he should complete his third degree from ��«Ӱҵ with a doctorate in computational science and statistics with a statistics specialization. He has presented at a national conference and had a paper printed in an academic journal.

However, when the East Bethel, Minnesota, native reflects on his time at SDSU, the strongest memories aren’t numbers, but people.

“In graduate school the difficulty of classes increases, but I ended up with a very good group of peers, four or five people who became very good friends. Two of them are also in a similar doctorate program. Not only do we share an interest in statistics, we’ve become good friends. I didn’t have that in my undergraduate experience,” Simpson said.

He said his relationship with the faculty in the math and statistics department has been equally as satisfying.

“The faculty has been so nice, and I don’t just have a relationship with just my adviser (Semhar Michael). There is a handful of faculty I have a relationship with. It’s a really good atmosphere, very much like a team, which is cool and, I think, kind of unique,” Simpson said.

Michael said, “The department's student-to-faculty ratio is well-balanced, ensuring that students have ample opportunities to engage and collaborate closely with faculty. This seems to reflect the overall culture at SDSU. In addition, Andrew’s strong work ethic and collaborative mindset make him an excellent student and a pleasure to work with.”

Started in computer science

Simpson started out as a computer science major but switched a few months into his sophomore year because “I liked the beauty and elegance that can come with doing math. One of the more attractive aspects of statistics is that you get to do a lot of theoretical mathematics to develop methods and then implement them via different programming languages. In that way, it is sort of the best of both worlds (computer science and math).”

His original plan was to get a bachelor’s degree and become a data scientist.

But he learned he could get a master’s degree with only an additional year of study. That seemed like an attainable sacrifice. During his master’s program, he started working with finite mixture modeling and fell in love with research.

“I just became super interested in research. It doesn’t even feel like work or school anymore, so it was obvious to do a doctorate,” said Simpson, who began his doctoral work in fall 2022.

Creating finite mixture models

He is slated to complete his doctorate in 2026 and then would like to work at solving defense and national security problems while working in academia or at a national laboratory.

First, he needs to finish his doctoral dissertation, which deals with finite mixture models. 

Simpson explained with finite mixture models there are multiple populations within a data set, for example, males and females. However, you don’t know who the males and females are. By using other data, such as height and weight, the statistician tries to determine statistical probabilities on who the males and females are.

A lot of Simpson’s work is in forensics statistics. He said a classic example is a burglar breaks into a business and shatters a window. A bunch of glass fragments are found at the scene, and then a suspect is arrested with glass fragments on the shoes. But did the fragment found on the shoe arise from the broken window at the business?

Statisticians can develop a “fingerprint” of the glass by comparing trace mineral elements found in each fragment. A statistical model is built to estimate the distribution of the minerals within the fragment at which point methods can be employed to compare it with other pieces of glass.

From there, “probabilistic statements can start to be made about the source of the glass fragments,” he said.

Simpson said, “The model could be used with any element — paint chips or aluminum powder from an explosive device. The investigator does something to get a measurement and numbers.  We see the data and work with that data. There are a lot of applications that we can apply the model to.”

From this work, Simpson wrote a paper that was published in the journal Statistical Analysis and Data Mining. It was his first entry into finite mixture models during his master’s program and remains a career highlight.

A model for keystroke dynamics

One area where he used finite mixture modeling is in keystroke identification.

He explained, “Keystroke dynamics are the time it takes one to press between keys on a keyboard. Since everyone has a slightly different typing rhythm, the user of a computer system can be identified by how they type. We can think of this as being similar to a fingerprint to unlock your phone or computer. 

“Since passwords are often compromised, monitoring keystroke dynamics can add an extra layer of security by detecting unusual keystrokes, at which point it may be assumed that unauthorized personnel are using the system. 

“Many current methods for building a model of a user’s keystrokes focus on the cases when there is a single user who has authorized access to the computer system. In real-life scenarios, this is not always the case. For example, a family computer or inside businesses or government agencies where many people may be authorized access to a system.”

In late 2022, Simpson wrote a paper focused on developing new methodologies to be able to adequately group or separate keystrokes and build a model of users keystrokes in which many users have access to the same system. 

“For example, if two people have authorized access to a system and it is unknown which user was using the system at any given moment, one would want to be able to separate all the keystrokes and say this set of keystrokes came from user one and this other set came from user two.”

He won best student paper award in the American Statistical Association’s Statistics in Defense and National Security section for the project. The award included a plaque and a $1,000 travel award to attend the association’s national conference.

The paper was published in the journal Statistical Analysis and Data Mining. It was his first entry into finite mixture models during his master’s program and remains a career highlight.

Worked in statistical consulting center

Simpson also spent August 2023 through May 2024 working under math department faculty members Hossein Moradi and Gemechis Djira in the SDSU Statistical Consulting Center.

He had a student employee position working with researchers who don’t have the technical knowledge to work through their data. He was working on a handful of projects at a time, primarily for ag and nursing researchers. 

“It was a cool experience to touch on a lot of fields and be able to switch your focus,” said Simpson, who stepped down to focus on his own research and to work with faculty members Chris Saunders and Michael on a National Science Foundation grant.

Moradi said of Simpson’s work, “Andrew did a great job working on multiple projects. He was statistically talented, professional and responsible with time to delivery and capable of sharing complex ideas to someone with limited exposure to statistics.” 

Outside of the math department, he likes to spend time with his young family. Simpson and his wife, Gabby, have a girl, Naia, 3, and a boy, Koa, 15 months. He also enjoys practicing Brazilian jiu-jitsu with a couple of his Ph.D. buddies.