DNA replication is a stochastic process with replication forks emanating from multiple replication origins. The origins must be licenced in G1, and the replisome activated at licenced origins in order to generate bi-directional replication forks in S-phase. Differential firing times lead to origin interference, where a replication fork from an origin can replicate through and inactivate neighbouring origins (origin obscuring). We developed a Bayesian algorithm to characterize origin firing statistics from Okazaki fragment (OF) sequencing data. Our algorithm infers the distributions of firing times and the licencing probabilities for three consecutive origins. We demonstrate that our algorithm can distinguish partial origin licencing and origin obscuring in OF sequencing data from Saccharomyces cerevisiae and human cell types. We used our method to analyse the decreased origin efficiency under loss of Rat1 activity in S. cerevisiae, demonstrating that both reduced licencing and increased obscuring contribute. Moreover, we show that robust analysis is possible using only local data (across three neighbouring origins), and analysis of the whole chromosome is not required. Our algorithm utilizes an approximate likelihood and a reversible jump sampling technique, a methodology that can be extended to analysis of other mechanistic processes measurable through Next Generation Sequencing data.