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Despite their outstanding performance in the majority of scenarios, contemporarylanguage models still occasionally produce undesirable outputs, for example, hallucinated text. While such behaviors have previously been linked to uncertainty,there is a notable lack of methods that actively consider uncertainty during textgeneration. In this work, we show how Minimum Bayes’ Risk (MBR) decoding, amethod that was originally designed to account for the imperfect nature of probabilistic language models, can be generalized into a principled uncertainty-awaredecoding method. In short, we account for model uncertainty during decodingby incorporating a posterior over model parameters into MBR’s computation ofexpected risk. We show that this modified expected risk is useful for both choosingoutputs and deciding when to abstain from generation. We benchmark differentmethods for learning posteriors and show that performance correlates with thediversity of the combined set of models’ predictions.