Kevin Cowtan kdc3 at
Tue Oct 28 11:42:09 EST 1997

Jonathan Ho wrote:
> Can anyone out there explain in layman's term what is the
> theory behind Maximumlikelihood refinement?  I tried reading
> and cannot really understand.  Thank you

Good question!

Well, I hope some more knowlegable people will have a go, but here is my

Assuming that we are just refining against magnitudes, then:

 Least squares refinement produces the model which most
 accurately reproduces the observed magnitudes.

 Maximum likelihood refinement produces the model which is
 most likely to have given rise the observed magnitudes.

Why are these different? Well, in practice we know that there are errors
in the measured magnitudes, and usually we have some estimate of these
errors. Least squares will try and introduce bogus features in the model
to try and reproduce those errors in the magnitude. Maximum likelihood
will only try and fit the data as well as the error estimates require,
and of the ensemble of possible model which could fit that criterion
will produce the most probable.


Dr. Kevin Cowtan, Protein Structure Group,           email cowtan at yorvic
University of York, York YO1 5DD. United Kingdom   

More information about the Xtal-log mailing list