Thanks to Petrus Zwart, Navraj Pannu, Marc Schiltz and Kevin Cowtan I've got a clearer idea as to what's going on (at least until I manage to confuse myself again).
>1. How does one determine the amplitude and phase to use from a given >likelihood surface? Some of the papers I've read refer to using the >centroid; others seem to be talking about using the location of the maxima. >Is there any guidance for when you'd use one instead of the other, or is >this one of those "try both and see which works best" situations? The unanamous response was to use centroids; so I was most likely misunderstanding things when I'd though I was reading about using likelihood maxima. >2. How do you get the HL coefficients out of a likelihood surface? The >only way I could think of to do this would be to pick up the likelihood >values over the full phaser circle for a constant amplitude, and fit a >2-term fourier series to the ln of those values. But this approach feels >more like a work-around than anything else (and would lead to the same >point in complex space having two difference likelihoods for a centric >reflection), so I'm fairly sure there's a better way to do this (although I >don't have any ideas what that would be). SigmaA weights might be a >possibility, but as far as I know they wouldn't work for all cases (MAD and >SAS don't have native amplitude measurements). This turns out to be a bit more complicated. Fourier series fitting (2 a terms and 2 b terms for acentrics; 1 a term and 1 b term for centrics) seems to be a usable approach. However using these HL coefficents would end up losing information, at least for acentrics (by going from a complex distribution to an angular distribution). One approach for avoiding this is to improve the approximation (as in Bricogne et al. 2003 Acta D59 2023-2030) with more coefficients, another is to avoid the need to pass information this way by incorporating multiple likelihood functions within a single program (as done in refmac5d (at http://www.bfsc.leidenuniv.nl/software/sadrefine/) ). Thanks again to all who responded, Pete Pete Meyer Fu Lab BMCB grad student Cornell University
