Martin Wells' research interests center on applied and theoretical statistics and sometimes cross the boundary into applied probability. He has worked on inference questions in credit risk, economic damages, epidemiology, finance (physical and risk neutral worlds), graphical models, legal studies, microarrays, proteomics, quantitative trait loci, extremes, data networks and has considered estimation problems for heavy-tailed phenomena. His theoretical research has focused on Bayesian statistics, biostatistics, conditional inference, evidence assessment, functional data, hypothesis testing, saddlepoint approximations, and shrinkage estimation.