The Geometry of Evidence: How Mathematical Thinking Shapes Public Health Decisions

Mathematics is the language we use to model and understand patterns in the natural and social world. Statistics is the branch of mathematics that transforms data into understanding—developing methods to collect, analyze, and interpret information, and to draw inferences about the world from limited evidence. Together, mathematics and statistics form a geometry of evidence: providing a framework for reasoning about the world when certainty is out of reach. In this keynote, we will explore that geometry, demonstrating how mathematical thinking guides public health and policy toward more effective and compassionate choices. I will begin by sharing my personal journey in the field of mathematics, including the last-minute change of direction that landed me where I am today – in the field of public health and biostatistics!! I will describe the key challenges I face in the work I do each day: trying to find reliable evidence in complex real-world settings so we can ensure the impact we have on policy and decisionmakers is meaningful and accurate. Such challenges include issues around missing data, constrained sample sizes, and questionable assumptions. I will showcase how I've used mathematical statistics – namely causal inference --  to shed light on some of these challenges by doing a deeper dive into two research highlights from my career: applying causal inference to rare disease research to understand how lifestyle factors may modify the course of illness and highlighting the benefits of using Bayesian inference to evaluate the potential of different gun policies to reduce deaths from firearm violence.  I will leave you with some reflections reminding us that beyond the equations and models lies a deeper responsibility for us as mathematicians.