Bootstrap in refinement

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Presentation transcript:

Bootstrap in refinement 28 March 2007 Bootstrap in refinement Gábor Bunkóczi

Computationally demanding! 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!

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

Bootstrap - algorithm Sample: Resampling: Refinement: Accumulation: 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

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

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

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