[BLML] Bridge or gambling? Art 12C1c revisited

richard willey richard.willey at gmail.com
Mon Dec 13 16:39:42 CET 2010

There is ample academic precedence for the methodology that you are

Conceptually, assigning a score seems very similar what’s known as a
“missing data” problem in statistics.

There’s a wide variety of different techniques used to handle missing data
problems (case-wise deletion, regression substitution, etc.) each with their
relative strengths and weaknesses.

The system that you’re suggesting is a degenerate case of what’s known as
“multiple imputation”.  (Typically, when you use multiple imputation, you
run a full blown Monte Carlo simulation rather than rolling your die once)

Here’s a more concrete illustration based on your original example

·         Roll your die 100 times and assign scores based on the number
shown on the d6

·         Compute the results of the match for each case

·         Average the results of all of the “virtual” matches

·         Set the results of the “real” match equal to this mean

[In simple examples like the one we’re discussing you can do this all
analytically rather than requiring a monte carlo]

Conceptually, the difference would seem to be whether we care about
estimating a plausible value for the individual board or for that match…

I think back to the halcyon dates of my youth, when indeterminate Hessians
had something to do with the Revolutionary War, where conjugate priors were
monks who had broken their vows, and the expression (X'X)^-1(X'Y) was greek

Those were simpler times
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