A series of *N* sequential configurations and their energies were
generated by a VMC calculation.
The *N* energies were divided up into *b* blocks
each containing energies. The average value for each block and
the variance of the block averages are then given by

When the block size is large enough such that the individual block
averages can be considered as being independent,
the value of might be expected to be inversely
proportional to .
This is because the individual error in the mean,
is proportional to . In an attempt to calculate
this constant of proportionality, the
*statistical inefficiency*, *s*, is defined as

It is possible to calculate a value for *s* from the *N* energies by
plotting the value of *s* for a series of block sizes.
Finally, from the definition of the
variance in the mean for a series of *N* values and a correlation
length , we have

It is clear that for the case of a single block that constitutes the
whole sample (i.e. ) *s* is equivalent to in
(). For the energies produced in a VMC calculation the
value of *s* proved to be much smaller than expected, about 2.8. This
meant that every third move of all the electrons could be written out
as an independent configuration. Where results are presented later in
this report for fitting with 1000 configurations this required a 3000
move VMC calculation, and 30,000 moves were required to generate 10,000
configurations.

Tue Nov 19 17:11:34 GMT 1996