Adaptive predictor combination (APC) is a framework for combining multiple predictors for lossless image compression and is often at the core of state-of-the-art algorithms. In this paper, a Bayesian parameter estimation scheme is proposed for APC. Extensive experiments using natural, medical, and remote sensing images of 8-16 bit/pixel have confirmed that the predictive performance is consistently better than that of APC for any combination of fixed predictors and with only a marginal increase in computational complexity. The predictive performance improves with every additional fixed predictor, a property that is not found in other predictor combination schemes studied in this paper. Analysis and simulation show that the performance of the proposed algorithm is not sensitive to the choice of hyper-parameters of the prior distributions. Furthermore, the proposed prediction scheme provides a theoretical justification for the error correction stage that is often included as part of a prediction process.