1 / 7

Bayesian Inference

Bayesian Inference. Consistency Extensability. Reproducibility. Standard approach to NMR structure determination. Minimize. E total = E empirical + λE experimental. Lagrange multiplier. Consistency. r obs – r calc. Conventional:. ì . 2. k. (. r. (. x. ). r. )). ,. r. (.

loren
Download Presentation

Bayesian Inference

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bayesian Inference • Consistency • Extensability Reproducibility

  2. Standard approach to NMR structure determination Minimize Etotal = Eempirical + λEexperimental Lagrange multiplier

  3. Consistency robs – rcalc Conventional: ì 2 k ( r ( x ) r )) , r ( x ) r - > max max ï ï C ( x ) 0 , r r ( x ) r í = £ £ min max ï 2 ï k ( r r ( x )) , r ( x ) r - < î min min Bayesian:

  4. Over-fitting Precision of NMR-derived protein structures Doreleijers, J.F., Rullmann, J.A.C. and Kaptein, R. (1998). J. Mol. Biol. 281, 149-164. More precise More observations

  5. A Bayesian approach Posterior probability = Likelihood * Prior probability Bayes rule

  6. Turning the conventional approach intoBayesian inference Bayes: Minimize the negative log-likelihood Restrained MD minimizes Correspondence: Bayesian restraint potentials Constrain: NOEs not distances J’s not dihedrals etc. Using a quadratic potential

  7. Significance of TRD 3: PINE • NMR needs to be more “Bayesian” • Relatively few rigorous approaches: MaxEnt, ISD (Nilges) • ModelFree comes close (maximum liklihood) • PINE+ Core • An API enabling Bayesian inference to incorporated into other packages

More Related