As highlighted by Kepler’s laws of planetary motion since the 17th century, mathematical modeling that describes observed data using simple formulas has deepened our understanding of various physical phenomena. However, observed data are often beyond our understanding in modern science, which makes full use of advanced measurement technologies to capture more complex phenomena. My grand challenge is establishing principles of modeling rooted in observed data to provide guidelines for understanding all phenomena without ambiguity. I am exploring the mathematics of a statistical method called Bayesian inference and promoting empirical research through collaboration with researchers from a wide range of natural sciences focused on condensed matter physics.