A new book by SPA Distinguished Professor Jeff Gill and co-author Le Bao (SPA PHD, ’22) seeks to introduce Bayesian statistical methods to readers with a single undergraduate statistics course.

Published by Cambridge University Press as part of its concise, digital, affordable Elements in Quantitative and Computational Methods for the Social Sciences series, Bayesian Social Science Statistics: Getting Productive is designed for students and researchers who may be curious about Bayesian analysis but lack the advanced mathematics typically associated with the field.

“Cambridge initially requested a single 100-page book,” said Gill. “My first reaction was that it couldn’t be done.” His most comprehensive Bayesian textbook, aimed at researchers and totaling 711 pages, assumes prior knowledge of matrix algebra, calculus, R, and Python.

At the time, Gill was supervising Bao’s dissertation; he is now an assistant professor at the City University of Hong Kong. When the publisher found their initial outline too expansive, they proposed dividing the material into two volumes.

The resulting books occupy what Gill describes as the accessible end of his work on Bayesian statistics. He and Bao developed ways to explain derivatives and integrals simply, while emphasizing that statistical software performs much of the computation. The book also addresses a broader problem in social science research: the tendency to treat statistical methods as a set of fixed recipes rather than as tools requiring critical judgment.

“Many social scientists learn a standard [methodological] approach in graduate school and then apply it throughout their careers without questioning its assumptions,” he said, leading to such pitfalls as the widespread use of significance stars. “For example, the null hypothesis significance test, the de facto method in the social sciences for testing hypotheses, is logically wrong. It's not just non-optimal: it's wrong.”

Bayesian statistics offers a different way of thinking about evidence. Rather than treating each study as an isolated test, Bayesian analysis begins with an existing distribution that represents prior knowledge or beliefs about a question. Researchers then use new data to update it, producing a posterior distribution reflecting what is known after considering the evidence.

“So we know stuff,” said Gill. “Then we get some data. Now we know some more stuff. That's the essence of Bayesian statistics, and that’s actually how science advances.”

Gill also sees Bayesian ideas as increasingly important to the future of science and technology, particularly because of their relationship to artificial intelligence and machine learning. Many AI systems rely on processes that update existing information when new data arrive. Further, Bayesian methods can improve transparency and incorporate multiple forms of knowledge instead of relying exclusively on a single sample that is contextual in space and time.

Indeed, the growth of Bayesian statistics has been closely tied to advances in computing. For much of the 20^th century, Bayesian and frequentist statisticians operated in sharply divided intellectual communities, with the latter arguing that Bayesian models could be mathematically difficult or impossible to estimate. The wider adoption of simulation-based techniques, particularly Markov Chain Monte Carlo (MCMC), changed that, allowing computers to approximate solutions to statistical problems too complex to solve by hand and opening the field to formerly impractical models. Researchers can now implement Bayesian analyses using R, Python, and specialized platforms such as JAGS, BUGS, and Stan.

The shift reflects a larger transformation in scientific research, as computing power fueled discovery in fields such as social science, biomedicine, and genetics.

“It freed the Bayesians,” Gill said. By placing Bayesian methods within reach of readers at the beginning of their statistical training, he and Bao hope to encourage more researchers to question inherited procedures and consider alternative ways of interpreting evidence.

The result is a guide intended not only to explain Bayesian statistics, but also to invite readers into a different philosophy of scientific reasoning—one in which existing knowledge, new evidence, and uncertainty are treated as parts of the same analytical process.

Bayesian Social Science Statistics: Getting Productive is available for purchase at Cambridge University Press.