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This study introduces a shared language for statistical and mathematical modeling using causal inference. It unifies quantitative science by formalizing connections between these distinct modeling traditions.

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Area of Science:

  • Quantitative Science
  • Interdisciplinary Modeling

Background:

  • Statistical and mathematical modeling traditions developed independently with distinct languages.
  • Advancing scientific knowledge is a common goal for both traditions.

Purpose of the Study:

  • To develop a shared language for statistical and mathematical modeling.
  • To formalize connections between these two quantitative traditions.
  • To advance interactions between different modeling approaches.

Main Methods:

  • Utilizes the concept of identification from causal inference.
  • Reviews foundational identification results for statistical models.
  • Extends identification concepts to mathematical models, employing bounds for analysis.

Main Results:

  • Establishes a framework using bounds for analyzing both statistical and mathematical models.
  • Illustrates the framework with a pharmacodynamic model for hypertension.
  • Provides a unified perspective for interpreting, comparing, and integrating diverse modeling approaches.

Conclusions:

  • Formalizes connections between statistical and mathematical modeling, creating a shared framework for quantitative science.
  • Highlights the potential for enhanced interactions between these modeling traditions.
  • Suggests future extensions for the proposed approach.