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Bootstrap in refinement

28 March 2007. Bootstrap in refinement. Gábor Bunkóczi. Bootstrap - basics. Statistical method for estimating the sample distribution of an estimator. Procedure: Given an estimator ( Ε ) and a sample. Create a new sample by resampling the original sample WITH replacement.

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Bootstrap in refinement

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  1. 28 March 2007 Bootstrap in refinement Gábor Bunkóczi

  2. Bootstrap - basics • Statistical method for estimating the sample distribution of an estimator. • Procedure: • Given an estimator (Ε) and a sample. • Create a new sample by resampling the original sample WITH replacement. • Calculate the estimator, store the value. • Repeat 1-3 Nboot times (> 1000). • Computationally demanding!

  3. Bootstrap - aims Model validation 1. R-factor distribution 2. Coordinate errors Map improvement 1. Bias removal 2. Resolution extension

  4. Bootstrap - algorithm Sample: Fo-Fc normalised in each resolution shell by <│Fo-Fc│2> Resampling: 1. Generate ΔFnorm = (Fo-Fc)/ Norm 2. Randomise: ΔFnorm→ΔFnorm, random 3. Calculate Fo = Fc + ΔFnorm, random * Norm Refinement: 1. Model randomisation 2. Refinement on “bootstrap” data 3. Calculate R/Rfree on original data Accumulation: 1. R-factors 2. Map coefficients

  5. Bootstrap - implementation START: Model, Dataset Initial refinement to calculate normalisation factor Generate “bootstrap” datasets Refinement Refinement Refinement Extract data from log files Accumulate map coefficient END: R-factor distribution, multiple models

  6. Bootstrap – results • R-factors: • distributions very tight • further randomisation increases absolute value but does not make the distribution broader • Coordinates:

  7. Bootstrap – development 1. Resample residuals → resample likelihood P(Fo, Fc) 2. Resample ΔF→ resampledifference map 3. Improved normalisation

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