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Link adaptation adjusts the optimal modulation and coding scheme (MCS) in response to a time-varying wireless channel. Current link adaptation techniques rely on carefully tuned heuristics and periodically reported channel quality index (CQI) values to maximize the link throughput under an externally defined block error rate (BLER) target. In this paper, we propose BayesLA, a Bayesian link adaptation scheme, which efficiently learns the CQI-dependent MCS success probabilities from the historical transmission success events. Our approach, which is inspired by the Thompson Sampling approach for machine learning, obviates the need to hand-tune link adaptation parameters in order to optimize for different physical layer configurations. We conduct numerical simulations for a cellular link over a Rayleigh fading wireless channel to demonstrate that BayesLA outperforms state-of-the-art outer loop link adaptation (OLLA) approach in terms of the realized link throughput for a given BLER target.