[QUANTITY] Why quantities always have errors

[owner-dm at eso.org]

Just a reminder that Quantities are effectively incorporated in the
Space-Time coordinate metadata schema.

Each coordinate value is essentially a Quantity, containing six
components:
- Name
- Value
- Error
- Resolution
- Size
- Pixel size

And each of these components has its own unit associated with it.
(This is a must - there are plenty of catalogs with positions in
degrees and resolutions or errors in arcsec)

The data type for components of scalar coordinates are simple doubles,
though one could imagine something more sophisticated for, say, Error
and Resolution.  Scalar coordinates are Time, Redshift, Spectral, and
1-D Spatial.
The exception is Time where the Value is of type AstronTimeType.
For vector coordinates (i.e., 2-D and 3-D spatial - position and
velocity) Value becomes a vector; the other components also may be
vectors but position angles or matrix desciptions are also allowed.
Clearly, one needs a mechanism to enforce consistency between the
dimensionality of the components of a Quantity.  Maybe Dimensionality,
a simple integer, should be the seventh component.

  - Arnold

Ed Shaya wrote:
[ Charset UTF-8 unsupported, converting... ]
> Need to add to my wish list:
> 
> 
> Errors can be given as a fraction or percentage of the value
> An Error can be for a value or for all the values.
> Errors may be generated by algorithm, as in sqrt(N).
> 
> Ed
> 
> Ed Shaya wrote:
> 
> >
> >  what things are going to be in the Error before we can know what sort 
> > of beast it is.  We should create a wish list of things that COULD go 
> > into an Error object.  Then we can go over it and strike things that 
> > are either too rare to bother with or just too complicated.  Here is 
> > my wish list:
> >
> > positiveError:  error bar to the plus side
> > negativeError:  error bar to the minus side
> > Error:  for symmetric error bars
> > sigma:  number of standard deviations that the  Error represents
> > confidence:  percentage confidence level that the Error represents
> > distributionFunction:  gaussian, laurentzian, hat-function, etc
> >
> > PgtV: Sometimes error is presented as the probability of exceeding  
> > the given value
> > PltV:  or not reaching the given value
> >
> > And, one may have the entire probability function as the quantity in 
> > the Error.
> >
> > All of the above for each of
> > randomError: Error resulting from finite precision of the measurement
> > systematicError:  inaccuracy intoduced by faulty equipment, 
> > calibration, or technique.
> > significantFigures: number of significant digits in the number
> >
> > We also need to deal with the issue of an upperLimit or lowerLimit, 
> > [which, by the way, usually does not have an error because it is 
> > either the error or a measured value plus an error.  But, it can have 
> > an error which is actually the error-on-the-error.]
> >
> > Ed
> >
> 
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Arnold H. Rots                                Chandra X-ray Science Center
Smithsonian Astrophysical Observatory                tel:  +1 617 496 7701
60 Garden Street, MS 67                              fax:  +1 617 495 7356
Cambridge, MA 02138                             arots at head.cfa.harvard.edu
USA                                     http://hea-www.harvard.edu/~arots/
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