We propose a novel scheme for detecting coded data transmitted over a communication channel that is either partially or entirely unknown. Viewing the unknown channel parameters as stochastic quantities drawn from a known probability distribution, the likelihood of a sequence of data is derived using Bayesian techniques. A stack-like tree search algorithm is proposed for implementation of maximum likelihood (ML) sequence detection under the Bayesian metric. We apply the Bayesian scheme to the binary symmetric channel (BSC) with unknown crossover probability. The structure of the resulting metric is compared to both the conventional Fano metric and a universal metric presented in (Lapidoth and Ziv, IEEE Trans. IT 1999). Based on its relationship to the metric developed by Lapidoth and Ziv, the newly-derived metric is shown to be pairwise universal over the ensemble of random uniform codes.