What Is Bayesian Modeling?

Environmental health scientists, like all of us, face a world of growing complexity. Answering complex research questions requires the right kind of analytical tools. One of the most powerful of these tools is Bayesian modeling. But what is it exactly, and what are its advantages?

The best way to understand Bayesian modeling is through an example. Let’s say we want to examine the risk of cardiovascular disease mortality across the United States at a fine geographical scale in groups exposed to a climate-related stressor, like a period of elevated heat, compared to those who haven’t been exposed. Perhaps simple enough for someone with environmental health training. But what if we want to add other elements—for instance, by looking at counties within states to analyze the impacts of state-specific climate policies and also the age-specific impacts on residents, drawing on data from neighboring age groups?

“A powerful way to answer a question like this is utilizing a Bayesian approach,” says Robbie M. Parks, assistant professor of environmental health sciences at Columbia Mailman School and instructor of a summer non-degree course on the subject offered through the Department of Environmental Health Sciences’ SHARP program. “Increasingly, environmental health scientists are relying on this kind of analytical framework to answer complex questions about exposures of all kinds.”

Bayesian modeling is able to incorporate prior knowledge into the model. In environmental health, this can be used to inform the model with information from previous studies, such as the previously estimated toxicities of certain pollutants. This allows for more predictions incorporating previous work, all while taking into account the uncertainty of these associations.

A particularly powerful advantage is Bayesian modeling’s ability to incorporate uncertainty. In environmental health, that may include uncertainty in the exposure, or prior knowledge about the association with the outcome. This approach incorporates model uncertainty, which can help estimate the probability of a hypothesis being correct. There are many other benefits, too, such as its flexibility in dealing with missing data. 

Finally, Bayesian modeling is a powerful tool for decision-making. It can be used to inform policy decisions by providing a quantitative assessment of a variety of complex risks associated with exposure to pollutants.

While Bayesian modeling is ascendant in environmental health sciences, particularly in the last decade, the theory underlying it is anything but new. In fact, the originally-stated Bayes’ theorem, which describes how to update the probability of a hypothesis as new evidence becomes available, is named for Reverend Thomas Bayes, an 18th-century statistician and theologian, who first described the theorem in a paper published posthumously way back in 1763.  

Parks’ two-day in-person training for environmental health scientists and other public health professionals will focus on the basics of Bayesian modeling, starting with examples of how to use the wealth of existing knowledge and software in the context of environmental health. Students learn through a combination of lectures and computing labs. 

(Register for the training here. Scholarships are available for early-career investigators. The scholarship application deadline is March 7.)

The course is one of 29 non-degree trainings offered this summer through the SHARP program. Other statistical trainings offered include Causal Mediation Analysis, Mendelian Randomization, Exposure Modeling, Machine Learning, Quantitative Genomics, Missing Data Workshop, and more. Additional SHARP trainings cover a variety topics, including a Multi-Omics Boot Camp, GIS Workshop, an NIH Grant Writing Boot Camp, Climate Change and Health Boot Camp, and more. 

“The need for new data modeling has increased exponentially, and in response, we’re offering these summer trainings and a new MS in Environmental Health Data Science,” says Andrea Baccarelli, chair of environmental health sciences at Columbia Mailman School. “Environmental health scientists are increasingly ambitious about the kinds of complex questions we seek to answer—because the world demands that we do so.”