Online education affords the opportunity to revolutionize learning by providing access to high-quality educational resources at low costs. The recent popularity of so-called MOOCs (massive open online courses) further accelerates this trend. However, these exciting advancements result in several challenges for the course instructors. Among these challenges is the detection of collaboration between learners on online tests or take-home exams which, depending on the courses' rules, can be considered cheating. In this work, we propose new models and algorithms for detecting pairwise collaboration between learners. Under a fully Bayesian setting, we infer the probability of learners' succeeding on a series of test items solely based on their response data. We then use this information to estimate the likelihood that two learners were collaborating. We demonstrate the efficacy of our methods on both synthetic and real-world educational data; for the latter, we find strong evidence of collaboration for a certain pair of learners in a non-collaborative take-home exam.