`All models are wrong but some are useful' (George Box 1979). But, how to find those useful ones starting from an imperfect model? How to make informed data-driven decisions equipped with an imperfect model? These fundamental questions appear to be pervasive in virtually all empirical fields -- including economics, finance, marketing, healthcare, climate change, defense planning, and operations research. This article presents a modern approach (builds on two core ideas: abductive thinking and density-sharpening principle) and practical guidelines to tackle these issues in a systematic manner.Comment: Final accepted version. The supplementary section contains some notes on the connections and differences between the Bayesian statistical approach vs. the Abductive statistical approach to model misspecification, robustness, and decision-making