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What functionality should exist in a CAS that was specifically geared toward Statistics?

Symbolic algebra systems like Mathematica and Maple are often used for calculus, logic, and physics problems but are rarely used for statistics. Why is this?

What statistical constructs could be added to a symbolic algebra system to improve its use in this field? What are some specific code samples that many people would like to be able to do.

Please think about the following three users: research statistician, non-statistics researcher using statistics in another field (such as biology), statistics student.

I'll be working on SymPy's statistics code over the next few months and would like to solicit input for desired functionality. The things I use are not necessarily what the broader community uses.

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  • $\begingroup$ There's a package dedicated to statistics, see R project for statistical computing (r-project.org). $\endgroup$
    – Roman Luštrik
    May 5, 2011 at 7:15
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    $\begingroup$ Yes, R is great for statistics. It tends to specialize in mostly numeric computations however. I'm interested in what we can do to assist researchers in symbolic manipulations. $\endgroup$
    – MRocklin
    May 5, 2011 at 18:07
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    $\begingroup$ It's not evident that any of these symbolic systems need "statistical constructs" added to them. Mathematica has done a lot of that in release 8, but it's still not likely to become a popular platform for applied statistics or students. One reason is that good stats software supports the non-mathematical labor much better than the math software does: data input, management, transformation, querying, and documentation. The stats software usually also supports a huge gallery of data visualization methods. $\endgroup$
    – whuber ♦
    May 6, 2011 at 4:39
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    $\begingroup$ I'm not sure why you think CAS is rarely used in statistics; personally I use Mathematica all the time. Casella & Berger even has an appendix devoted to Mathematica. But as a statistician I generally spend more time with data than doing math, like @whuber points out. $\endgroup$
    – JMS
    May 6, 2011 at 20:12
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    $\begingroup$ Also recognize that many (most?) academic researchers and students have free access to mature packages like Maple and Mathematica through uni machines and/or site licenses. $\endgroup$
    – JMS
    May 6, 2011 at 20:17

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Support for matrix algebra. The vast majority of practiced statistics is multivariate and involves matrices, and often simplifying matrix forms requires special rules that aren't easily translated from a univariate case, so good matrix support would be really helpful.

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    $\begingroup$ This is something Mathematica is good at already. $\endgroup$
    – whuber ♦
    May 4, 2011 at 23:34
  • $\begingroup$ Excellent point. What could be added to a system that already expressed linear algebra well? Or is a solid expression of matrices sufficient? $\endgroup$
    – MRocklin
    May 6, 2011 at 4:05
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    $\begingroup$ @MR Rather than ask what could be added to these systems, think about why you're doing this. For whom? What uses to you want to support? What are the compelling reasons (if any) to be adding statistical procedures to a symbolic system? In other words, begin with a good functional specification. $\endgroup$
    – whuber ♦
    May 6, 2011 at 4:42

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