In the era of “big data”, analysts usually
explore various statistical models or machine learning
methods for observed data in order to facilitate scientific
discoveries or gain predictive power. Whatever data and
fitting procedures are employed, a crucial step is to select
the most appropriate model or method from a set of
candidates. Model selection is a key ingredient in data
analysis for reliable and reproducible statistical inference
or prediction, and thus central to scientific studies in
fields such as ecology, economics, engineering, finance,
political science, biology, and epidemiology. There has
been a long history of model selection techniques that
arise from researches in statistics, information theory,
and signal processing. A considerable number of methods
have been proposed, following different philosophies and
exhibiting varying performances. The purpose of this
article is to bring a comprehensive overview of them,
in terms of their motivation, large sample performance,
and applicability. We provide integrated and practically
relevant discussions on theoretical properties of state-ofthe-art model selection approaches. We also share our
thoughts on some controversial views on the practice of
model selection
