We recently implemented a Bayesian statistics and sampling algorithm approach for structural refinement using diffraction data. This was a really fun collaboration with some statisticians and mathematicians, and is an area in which we are still working. The paper can be viewed here: http://www.nature.com/articles/srep31625 The NC State press release is here and was picked up by the following news outlets already:
- Nanowerk: http://www.nanowerk.com/nanotechnology-news/newsid=44291.php
- Phys.org: http://phys.org/news/2016-08-approach-atoms-materials.html
In a different project, one of IRES summer research students (Alexandra Larsen) created an introductory tutorial on Bayesian statistics for the non-expert (i.e., materials researchers). It can be found here: https://www.youtube.com/watch?v=S_ItC4ytT60.