__Experimental phasing by maximum likelihood__

__Outline__

This page will be expanded at some point. At the moment, it is mostly a placeholder
for some animations illustrating the likelihood function used for multiple isomorphous
replacement phasing, and how that likelihood function varies as parameters are
varied.

__The concept of likelihood__

## Joint distributions of structure factors

## MIR likelihood function

__MIR likelihood as a function of refined parameters__

## Likelihood as a function of heavy atom model

This animation shows the behaviour of the MIR likelihood target as a function
of the heavy atom model, illustrated by increasing the size of the heavy atom
contribution for the second derivative. The top left panel shows the Harker
construction, in which the origin of the second derivative circle (blue) changes
as the heavy atom contribution changes. In the top right panel, the Harker construction
is overlaid with the contours showing the product of the probabilities for the
three observations (native and two derivatives), as a function of the assumed
true native structure factor. The lower left panel shows the same product, now
multiplied by the prior probability of the true native structure factor, as
a surface plot instead of a contour plot. The volume under this surface (*i.e.*
the integral over the true native structure factor) is the MIR likelihood, shown
as a function of the heavy atom structure factor in the bottom left panel.

## Likelihood as a function of lack-of-isomorphism error

This animation shows the behaviour of the MIR likelihood target as a function
of the lack-of-isomorphism error assumed for the second derivative. The layout
is similar to the figure above, except in this figure the probability for the
second derivative observation is shown as contours in the top left panel. As
the lack-of-isomorphism error increases, the distribution becomes broader and
the likelihood increases, reaching a peak when the lack-of-isomorphism error
is just enough to provide a good overlap with the other circles.

© 1999-2005 Randy
J Read, University of Cambridge. All rights reserved.

Last updated:
7 June, 2005