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Data is a central reason for data analysis. The recent trend towards data science has lead to an interesting take on the intersection of statistics, mathematics, computer science and philosophy.

With that, we need to think through the many components of data analysis. Initially, we need to consider the hierarchy of storage structures, from completely general, to completely specified.

Data element TYPES can be based on COMPUTER SCIENCE principles, or inherit also STATISTICAL principles, and often both.

  1. LISP:ARRAY : a general random access lisp array.

    a. AREF is the common tool for access (element-wise)

    b. … is the common tool to create

  2. XARRAY : a variant which offers support for complex subsetting as well as crafting new arrays. Could use various (suboptimal) storage backends, including LISP:ARRAY. Commonly accessed by row number and column number.

    a. XREF is the common tool for access

    b. XCREATE is common tool for creation.

  3. ModelFrame (also known as a dataframe): column-typed storage, where column types can be any STATISTICAL type. Commonly accessed by variable name and/or subject id (key, id).

    a. XREF could be a common tool to access

    b. XCREATE could be a common tool to creation

    c. XSLICE could be a common tool for subsetting, reshapeing

    (what to use to put it all back together?). The KEY POINT for this object is the ability to take a ModelFrame along with a model specification and produce matrices and functions which can be computed with, which carry along (actual, or pointers back to) meta information (variable names, subject IDs) so that the results can be appropriately interpreted.

  4. numerical matrix: whole-array-typed storage, where the storage type is homogeneous

    a. MREF, XREF, AREF could be used for access, depending on underlying tool kit.

    b. ?? could be used to create.

At this stage (<2014-02-26 Wed>) I still need to resolve the above heirarchy.

Commonly used numerical systems tend to have 1,4 – with no means to really handle 3.

For me (AJ Rossini) the key to a statistical analysis system are the requirements in 3. Which is what makes R and XLispStat prototypes of this genre. But MATLAB and Julia are not so much, as they are more targetted for technical and numerical data analysis.