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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. (.

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Bayesian Inference

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  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

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