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Leonard has 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 is also known for his work concerning the applications of Bayesian methodology in geophysics, medicine, psychometrics and the provision of statistical expertise in legal cases. He was one of the founders, in 1992, of the International Society for Bayesian Analysis, alongside Arnold Zellner and Gordon Kaufman, and has published a history of the Bayesian approach.
Leonard is the co- author of Bayesian Methods: An analysis for Statisticians and Interdisciplinary Researchers with John S. J. Hsu and author of the sci-fi socio-political satire 'The Grand Oligarchs of Qinsatorix'.During December 2016, Leonard's interview by Diego Andres Peres Ruiz was published by the Bulletin of the International Society for Bayesian Analysis.