Predictive models are statistical models whose primary purpose is to predict other observations of a system optimally, as opposed to models whose purpose is to test a particular hypothesis or explain a phenomenon mechanistically. As such, predictive models place less emphasis on interpretability and more emphasis on performance.
Wikipedia has articles https://en.wikipedia.org/wiki/Predictive_modelling and https://en.wikipedia.org/wiki/Predictive_analytics with further references.
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