Indicators

[Peter Cameron]

As I understand things (and I know I will be corrected if I am wrong):
the reason that statisticians were interested in partial balance (in
the association scheme form, and later in the Jordan algebra form)
is that it eased the problem of inverting large matrices. Presumably
this is less of an issue now: just throw them onto the computer.

So if statisticians don't care about this concept any more, should
we even mention it? I think we should, for two reasons.

First, although statisticians invented association schemes, they
were invented independently by group theorists and by people working
on graph isomorphism, and have subsequently found use in such areas
as coding theory and knot theory. So, if an association scheme is
intimately connected with a design in some way, why not give this
information?

Second, as I have tried to explain in an earlier posting, although
not every symmetric matrix "lives" on an association scheme, every
matrix lives on a unique coarsest coherent configuration, and every
symmetric matrix lives on a unique coarsest symmetric Jordan 
configuration. So we can deal with concurrence, variance, and weighted
information matrices with the same conceptual set-up, and don't
really need to agonise over whether anyone really needs this data
for the weighted information matrix.

As a non-reason (but still of some interest I think), this analysis
raises various questions on which interesting research could be done.

Peter.