[1] During Leonard's tenure (1980–1995) at the Department of Statistics at the University of Wisconsin-Madison,[2][3][4] he worked on improving the Bayesian components of both the teaching and research programs, alongside Kam Wah Tsui and Michael Newton.

Leonard published on the Bayesian approach to categorical data analysis, as well as on function smoothing and prior informative density estimation, conditional Laplacian approximations for marginal inference and prediction, and the statistical modelling of log covariance matrices.

He was one of the founders, in 1992, of the International Society for Bayesian Analysis, alongside Arnold Zellner and Gordon Kaufman.

[5][6] Leonard's books include A Course in Categorical Data Analysis[7] and Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers, the latter co-authored with his former doctoral student, John S. J. Hsu,[8][9] At the University of Edinburgh, Leonard collaborated with Ian Main, Orestis Papasouliotis and others on publications in geophysics.

[10][11] He was also active during this period in the field of family medicine, contributing to articles on prevention of substance use disorders.