In practical statistical causal discovery (SCD), embedding domain expert knowledge as constraints into the algorithm is significant for creating consistent meaningful causal models, despite the challenges in systematic acquisition of the background knowledge. To overcome these challenges, this paper proposes a novel methodology for causal inference, in which SCD methods and knowledge based causal inference (KBCI) with a large language model (LLM) are synthesized through ``statistical causal prompting (SCP)'' for LLMs and prior knowledge augmentation for SCD. Experiments have revealed that GPT-4 can cause the output of the LLM-KBCI and the SCD result with prior knowledge from LLM-KBCI to approach the ground truth, and that the SCD result can be further improved, if GPT-4 undergoes SCP. Furthermore, by using an unpublished real-world dataset, we have demonstrated that the background knowledge provided by the LLM can improve SCD on this dataset, even if this dataset has never been included in the training data of the LLM. The proposed approach can thus address challenges such as dataset biases and limitations, illustrating the potential of LLMs to improve data-driven causal inference across diverse scientific domains.

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