In the era of big data, analysts usually explore various statistical models or machine-learning methods for observed data 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 it is central to scientific studies in such fields 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 has been proposed, following different philosophies and exhibiting varying performances. The purpose of this article is to provide 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-of-the-art model selection approaches. We also share our thoughts on some controversial views on the practice of model selection.
Bibliographical noteFunding Information:
This research was funded in part by the Defense Advanced Research Projects Agency under grant W911NF-18-1-0134. We thank Dr. Shuguang Cui and eight anonymous reviewers for giving feedback on the initial submission of the manuscript. We are also grateful to Dr. Matthew McKay and Dr. Osvaldo Simeone for handling the full submission of the manuscript, and to three anonymous reviewers for their comprehensive comments that have greatly improved the article.