Kant's transcendental idealism and statistics are closely related

Immanuel Kant argued that things in themselves cannot be known, and that human cognition is limited to phenomena. However, this is merely a misunderstanding resulting from a lack of quantification. This paper shows that Kant's transcendental idealism can be naturally reformulated as an estimation problem in statistics, and makes clear that things in themselves are the subject of estimation. Statistics has a weakness in that it lacks philosophical relevance. To solve this, the author proposes a highly abstract theory called "quantum language." However, considering its widespread use, I would like to realize it in a concrete way, "statistics + Kantian philosophy." I believe that these two methods are ultimately the same, but this paper is the result of research that takes the latter position.