Large language models primarily rely on inductive reasoning for decision making. This results in unreliable decisions when applied to real-world tasks that often present incomplete contexts and conditions. Thus, accurate probability estimation and appropriate interpretations are required to enhance decision-making reliability. In this paper, we propose a Bayesian inference framework called BIRD for large language models. BIRD provides controllable and interpretable probability estimation for model decisions, based on abductive factors, LLM entailment, as well as learnable deductive Bayesian modeling. Experiments show that BIRD produces probability estimations that align with human judgments over 65% of the time using open-sourced Llama models, outperforming the state-of-the-art GPT-4 by 35%. We also show that BIRD can be directly used for trustworthy decision making on many real-world applications.

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