This paper presents Bayesian Representation-based Classification (BRC), an approach based on sparse Bayesian regression and subspace clustering for image set classification. Similar to existing representation-based approaches such as Sparse RC (SRC) and Collaborative RC (CRC), BRC assumes that a test image is approximated by a linear combination of the gallery images of the true class. However, we show through a Bayesian statistical framework that BRC employs precision hyperpriors that are more non-informative than those of CRC/SRC, while also showing that CRC and SRC are identical up to an implicit choice of different precision hyperpriors. Furthermore, we analyze the assumptions of existing strategies for selecting the images to classify from a probe set (e.g. sequence mean) and we show that these strategies can still work under milder assumptions. Finally, we present a more robust probe set handling strategy that balances efficiency and accuracy. Experiments on three datasets illustrate the effectiveness of our algorithm compared to state-of-the-art set-based methods.