MatBYIB performs Bayesian inference on gravitational wave signals from inspiraling binary systems with arbitrary eccentricity, focusing on extreme mass-ratio inspirals. Written in MatLab, it generates analytical kludge waveforms, samples the parameter space (including masses, eccentricity, and spin) using a Metropolis–Hastings MCMC scheme, and tracks convergence with the Gelman–Rubin criterion and parallel chains. The code reads configuration parameters from a simple input file, then computes time- and frequency-domain waveforms, posterior distributions, and convergence diagnostics, and produces visualizations for all of these outputs.