Procurement maturity becomes a crucial indicator reflecting how effectively and efficiently a procurement function fulfills the expectations. Purchasing and supply management literature posits several maturity evalu-ation models providing tools for a comprehensive assessment of excellence. Quality management literature also handles that excellence issue from the process improvement perspective. This study investigates the role of process improvement practices in improving the maturity level of procurement organizations. A maturity assessment survey collects data from 96 purchasing and supply management professionals. We suggest a Bayesian hierarchical mean difference model that deploys a Markov Chain Monte Carlo (MCMC) sampler in inferring posterior parameters. Results indicate that firms regularly practicing process improvement activities have statistically higher performance than rarely or never practicing firms on aggregate procurement maturity and its sub-dimensions. These results emphasize that process improvement escalates procurement maturity from reactive to proactive level. As a novel branch of data science, we discuss the advantages of Bayesian hypothesis testing with the probabilistic programming approach compared to the traditional frequentist hypothesis testing.