1. Bootstrap in refinement
28 March 2007
Bootstrap in refinement
Gábor Bunkóczi

2. 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!

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

4. 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

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: Coordinates: 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 → resample difference map
3. Improved normalisation