Madigan received his bachelor's degree in mathematics (1984, First Class Honours, Gold Medal) and a Ph.D. in statistics (1990), both from Trinity College Dublin.

His Ph.D. thesis, titled An Investigation of Weights of Evidence in the Context of Probablilistic Expert Systems, was written under the supervision of Krzysztof Mosurski.

[6] Madigan has also served as Vice President, Data Mining, Soliloquy, Inc. (2000-2001), Principal Technical Staff Member, AT&T Labs-Research (1999-2000), Information Technology Consultant, KPMG (1989-1990), Technology Manager, Peregrine Expert Systems Ltd. (1986-1989), Expert System Consultant, SkillSoft, (1985-1986), and Actuarial Associate, Hibernian Life Assurance, Ireland (1984-1985).

He has over 200 publications[13] in such areas as Bayesian statistics, text mining, Monte Carlo methods, pharmacovigilance and probabilistic graphical models.

[14] In recent years he has focused on statistical methodology for generating reliable evidence from large-scale healthcare data.