Re: Dilemma deciding on 'best' process

["Timo Mäkeläinen" <Timo.Makelainen@Helsinki.fi>]

On 28 May 2003, at 13:14, Nicholas Kormanik wrote:

> 
> I'm analyzing a number of various processes, trying to find the one
> that consistently results in the highest outcome.  Below is a subset
> of results. Case Mean StDev SEMean  Q1  Median   Q3   SSQ
> SkewnessKurtosis CV 1    5.07  3.63  0.39  2.61  5.06   6.92  3411  
> 0.43   0.33  0.72 2    5.02  3.66  0.52  3.17  4.63   6.60  1876  
> 1.02   3.29  0.73 3    4.14  3.14  0.50  1.98  4.69   5.28  1042  
> 0.37   1.39  0.76 4    3.50  2.66  0.48  1.86  3.02   5.33   591  
> 0.67   0.68  0.76 5    3.70  2.89  0.32  1.18  3.60   5.96  1778  
> 0.04  -0.69  0.78 6    3.49  2.78  0.43  1.16  3.40   5.66   829 
> -0.62   0.65  0.80 7    3.76  3.00  0.55  1.20  3.85   5.85   683  
> 0.24  -0.64  0.80 8    4.91  3.95  0.37  2.57  4.43   6.59  4591  
> 1.22   2.28  0.80 9    7.67  6.17  0.94  2.45  8.23  11.84  4126 
> -0.02  -0.68  0.80 10   4.11  3.39  0.24  1.89  4.31   5.92  5457  
> 0.13   2.54  0.82 11   4.11  3.40  0.44  2.25  4.21   6.26  1695  
> 0.08   0.40  0.83 12   6.28  5.32  0.89  1.86  6.20  10.55  2410  
> 0.38  -0.02  0.85 13   3.76  3.19  0.36  1.41  4.22   5.79  1910 
> -0.03  -0.40  0.85 14   3.35  2.85  0.27  1.42  3.42   5.30  2215 
> -0.01   0.27  0.85 15   7.50  6.42  0.90  3.42  7.68  12.57  4925 
> -0.44   0.37  0.86 16   3.85  3.34  0.38  1.10  4.36   5.53  1965  
> 0.12   0.12  0.87 17   6.14  5.38  0.98  2.47  4.76   7.25  1972  
> 1.24   1.19  0.88 18   6.90  6.05  0.67  1.37  6.08  11.28  6871  
> 0.64  -0.46  0.88 19   7.11  6.25  0.81  2.24  7.58  11.23  5340  
> 0.06  -0.49  0.88 20   5.75  5.06  0.96  1.12  5.61   8.63  1615  
> 0.99   1.90  0.88 My tentative hunch is to use the last column ---
> Coefficient of Variation --- as the over-riding criterion.  Thus case
> number 1 is the best.
> 
> The first-impression-approach of simply using the highest Mean, case
> number 9, would appear to be a grave mistake, as the dispersion of
> outcome is so great.
> 
> Please comment on the above thinking.  Do you agree?  Or am I
> disregarding something important?
> 

The CV is a measure of relative dispersion (and not of location) so it
is indeed quite different from the mean. 

However, the meaning of "... consistently results in the highest  outcome" could be clarified in terms of loss functions. 

For instance the loss, linear in two pieces, (for suitable constants  b, c >0) 

L(t, a) = b*(a - t) for a >= t and 
L(t, a) = c*(t - a) otherwise 

where 't' is a target value and 'a' an action leads to the choice of 'a'  as the c/(b+c)-quantile of the distribution of 't'. 

The Bayesian setting in which 't' has either a posterior distribution  or a predictive distribution is a possibility.

> Thank you for your time and attention.
> 
> Nicholas
> 
> Salt Lake City, Utah
> 

Best wishes,

Timo M.

Timo Makelainen
Majavatie 12 A 7
FI-00800 Helsinki
Finland