In this paper, we investigate anomalous interactions of the Higgs boson with heavy fermions, employing shapes of kinematic distributions. We study the processes , , , and and present applications of event generation, reweighting techniques for fast simulation of anomalous couplings, as well as matrix element techniques for optimal sensitivity. We extend the matrix element likelihood approach (MELA) technique, which proved to be a powerful matrix element tool for Higgs boson discovery and characterization during Run I of the LHC, and implement all analysis tools in the JHU generator framework. A next-to-leading-order QCD description of the process allows us to investigate the performance of the MELA in the presence of extra radiation. Finally, projections for LHC measurements through the end of Run III are presented.