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I am somehow confused by the term of so called "predictive analytics". It is so often used today that makes me think the old-school statisticians never before tried to create any predictive models.

My thinking is that statisticians can do all that predictive modelers can and more, while predictive modelling focuses only on prediction part of the statistics and disregards descriptive statistics.

What are the areas where predictive analytics shine and statistical analysis will not be sufficient?

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I think you're reasoning from a false premise: statisticians and predictive modelers are not mutually exclusive. The difference between statistician and predictive modeler is just a matter of specialization. Your question is kind of akin to asking when Bayes' rule is better than probability -- Bayes rule is a specific application of probability.

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There are many people re-brand things, and try to re-market it to other people do not understand the topic in depth. The goals are giving impression that we are doing things very new and the state of the art. Statistics definitely do predictions all the time.

If you have time you can read the first chapter of deep learning book, and you can see how people use different terms to describe the same thing.

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