There have been a lot of questions and comments about Relion recently, so I thought it was worth a brief post. You'll note that it is now possible to "seed" a relion refinement with the results of an EMAN2 refinement for comparative purposes. Of course, philosophically, there is nothing wrong with the concept of maximum likelihood, and it produces extremely useful results in many fields. However, the way ML is currently handled in cryo-EM has a number of shortcomings, which makes it, in the end, pretty much equivalent results-wise to current methods, but far more computationally expensive. The shortcomings I see with current ML implementations:
1) Assumption that all particles are "good" and that they are equally "good", which is demonstrably untrue
2) Assumption that noise is independent & Gaussian in real and/or Fourier space - while this may be true for the noise coming from the microscope/detector, the reconstruction algorithm also sees as noise anything in the physical specimen which isn't a perfect particle. This component of the noise is often dominant, and is highly structured.
3) When the data is good, the orientations should settle on one specific value anyway. ie- if a particle really is probabilistically spread out in orientation space, it probably has no business going into the reconstruction anyway. That is, the only benefit you get out of ML in cases where the orientations are unique is that the local "smearing" due to slight local angular uncertainty is integrated into the answer. This can be taken into account without doing a full ML integral.
Anyway, here is a quick comparison from a poster in Tahoe last week. Clearly such comparisons are specimen and data-quality dependent, but it does illustrate some of what I'm trying to say in a practical way. Structures are presented as they were produced directly by the corresponding program, without additional filtration, note also that the EMAN2 result is done with speed=1, which provides a slight resolution boost at the cost of some CPU time. A ~8.4 Å map (vs the ~7.8 Å maps below) can be done in EMAN2 in 3-4 CPU-hours. Also note that FreAlign can do a bit better than shown in mode 4, but it takes a lot longer to run, and we didn't have a chance to do it before the poster was printed: