  Faced with complex problems, the human brain demonstrates a remarkable
capacity to transcend sensory input and form latent understandings of perceived
world patterns. However, this cognitive capacity is not explicitly considered
or encoded in current large language models (LLMs). As a result, LLMs often
struggle to capture latent structures and model uncertainty in complex
compositional reasoning tasks. This work introduces a novel Bayesian prompting
approach that facilitates training-free Bayesian inference with LLMs by using a
verbalized Probabilistic Graphical Model (PGM). While traditional Bayesian
approaches typically depend on extensive data and predetermined mathematical
structures for learning latent factors and dependencies, our approach
efficiently reasons latent variables and their probabilistic dependencies by
prompting LLMs to adhere to Bayesian principles. We evaluated our model on
several compositional reasoning tasks, both close-ended and open-ended. Our
results indicate that the model effectively enhances confidence elicitation and
text generation quality, demonstrating its potential to improve AI language
understanding systems, especially in modeling uncertainty.
