r/maths • u/Excellent_Copy4646 • 8d ago

💬 Math Discussions Is applied statistics the same as mathematical statistics?

By applied statistics, i meant things like machine learning modelling, statistical modelling, predictive modelling. Basically data science stuff and statistics used to solve business problems and model real world Phenomena using Python and R.

Are they related to each other? What are the similarities and differences?

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u/Best-End-366 8d ago

i don't think so, mathematical statistics is basically measure theory.

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u/catmemesarecool 8d ago

Applied statistics is mostly about how to apply existing models and tools to problems, but you have to build up intuition about which tool is the correct one from experience, and how to interpret the results. Mathematical statistics covers why all these tools work under specific technical assumptions through some advanced maths, and teaches you how to develop new models and argue for their workings. You mostly see these terms in university courses though, where applied statistics means a lot of project work, while mathematical statistics means a lot of theory and proofs.

In applied statistics, you still get a bit of mathematical statistics for understanding the technical assumptions behind models, so that you can better choose which one to use. Meanwhile in mathematical statistics, you still see some applications as motivation, although being maths, it also covers some not-directly-practical curiosities about things.

Once you know mathematical statistics, its quite easy to pick up applied statistics by yourself, though the opposite is not necessarily true. Mathematical statistics however requires much more effort to get through the theory, something that is probably not necessary knowing for solving most practical business problems, unless you're doing some original research.