Prognostics is the area of research that is concerned with predicting the remaining useful life of machines and machine parts. The remaining useful life is the time during which a machine or part can be used, before it must be replaced or repaired. To create accurate predictions, predictive techniques must take external data into account on the operating conditions of the part and events that occurred during its lifetime. However, such data is often not available. Similarity-based techniques can help in such cases. They are based on the hypothesis that if a curve developed similarly to other curves up to a point, it will probably continue to do so. This paper presents a novel technique for similarity-based remaining useful life prediction. In particular, it combines Bayesian updating with priors that are based on similarity estimation. The paper shows that this technique outperforms other techniques on long-term predictions by a large margin, although other techniques still perform better on short-term predictions.