  Breiman's classic paper casts data analysis as a choice between two cultures:
data modelers and algorithmic modelers. Stated broadly, data modelers use
simple, interpretable models with well-understood theoretical properties to
analyze data. Algorithmic modelers prioritize predictive accuracy and use more
flexible function approximations to analyze data. This dichotomy overlooks a
third set of models $-$ mechanistic models derived from scientific theories
(e.g., ODE/SDE simulators). Mechanistic models encode application-specific
scientific knowledge about the data. And while these categories represent
extreme points in model space, modern computational and algorithmic tools
enable us to interpolate between these points, producing flexible,
interpretable, and scientifically-informed hybrids that can enjoy accurate and
robust predictions, and resolve issues with data analysis that Breiman
describes, such as the Rashomon effect and Occam's dilemma. Challenges still
remain in finding an appropriate point in model space, with many choices on how
to compose model components and the degree to which each component informs
inferences.
