The high autocorrelations were caused by the shape of the
posterior distribution, which was a diagonal ridge (approximately
cigar shaped) in ( 
).
In order to sample more efficiently, the m and 
variables
were transformed. An alternative basis 
as
outlined in Section 
, would allow the routine move
more efficiently through the posterior.
The transformation takes the form of 
. Sampling from 
allowed much better
mixing for the chains, required less thinning of the results and
so yields faster run times.