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The Bayesian framework offers a number of techniques for inferring an individual's knowledge state from evidence of mastery of concepts or skills. A typical application where such a technique can be useful is Computer Adaptive Testing (CAT). A Bayesian modeling scheme, POKS, is proposed and compared to the traditional Item Response Theory (IRT), which has been the prevalent CAT approach for the last three decades. POKS is based on the theory of knowledge spaces and constructs item-to-item graph structures without hidden nodes. It aims to offer an effective knowledge assessment method with an efficient algorithm for learning the graph structure from data. We review the different Bayesian approaches to modeling student ability assessment and discuss how POKS relates to them. The performance of POKS is compared to the IRT two parameter logistic model. Experimental results over a 34 item Unix test …