You have to be able to think abstractly and counter-factually and mathematical training likely is the best way to obtain and hone those skills (1).

But most mathematical techniques applicable in statistics can be adequately approximated by various computations including simulation which suggests many topics can be skipped over or forgotten (students in stats course can’t because that how their current taught and tested).

On the other hand, anything that one can do mathematically that is not true for all sample sizes (perhaps greater than finite k) will require subsequent for my sample sizes verification by simulation – so simulation and computation cannot be skipped over or forgotten.

Of course you can’t do more with less, so math should be an advantage (but again 1).

1. “I have found mathematicians to be, by far, the best reasoners of any social class that excludes them; and yet it seems that an exclusive absorption in their studies, which more than any others demand exclusive devotion, tends to blind them to other kinds of reasoning.” Peirce ON THE FOUNDATION OF AMPLIATIVE REASONING 1910

Crudely put, they they often would rather do math than profitably apply statistical reasoning. This seem to include not wanting to do simulations. In particular, I have been wondering why Bayesians for so many years have not been simulating data from the prior and seeing if it emulates the world they are trying to model. Dan Simpson wrote a very recent paper noting priors often used when simulated from, gave air densities most often more dense that concrete. https://statmodeling.stat.columbia.edu/2018/09/12/against-arianism-2-arianism-grande/

Why did someone not do that 10, 20, 30 years ago?

]]>Here’s the U. Maryland PhD requirements for CS:

Coursework: Six graduate-level courses covering four areas out of artificial intelligence, bioinformatics, systems, databases, scientific computing, software engineering and programming languages, theory, and visual and geometric computing, and two more graduate courses from any area.

A person interested in the basic issue of statistical inference could take courses in AI, databases, scientific computing, and either software engineering/programming languages or bioinformatics.

The masters-level statistics program at UMD requires STAT650 Applied Stochastic Processes (3 Credits), Mathematical statistics (6 hours), Linear statistical Models (3 credits), plus some other credits.

At UMD The statistics program is much more focused on foundational mathematical concepts rather than topics such as database organization or programming.

At different universities the programs will vary. It probably makes sense to look at the specific requirements of the programs one is interested in. However, it will be generally true that computer science is bigger tent than statistics—with a wider range of topics studied in the field and required for graduate students.

]]>Also concur w/ above suggestions that you work or do a MS; a PhD is a long commitment and I definitely wouldn’t encourage anyone to apply until you are almost certain (you can’t be totally certain) that it’s exactly what you want to do.

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