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UBOAT

This document outlines a statistical approach for analyzing X-ray intensity data in crystallography using Bayesian statistics. It details a method to convert input intensities (I's) to output intensities (F's) and highlights how negative input intensities produce positive output intensities. Key calculations include the determination of statistical moments, the Wilson plot, and cumulative intensity distributions to detect anisotropy. Additionally, it discusses future work involving twinning and advanced data analysis techniques. The insights presented are foundational for understanding intensity distribution in crystallographic studies.

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UBOAT

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  1. UBOAT Norman Stein CCP4 Daresbury Laboratory York 27/3/07

  2. TRUNCATE replacement • Converts I’s to F’s • Negative input I’s give positive output I’s, F’s • Calculates Statistics: Moments of I Wilson plot Cumulative intensity distribution Detection of anisotropy (Yorgo Modis)

  3. Mathematical Detail • Use Bayesian statistics • Combine prior knowledge and observations to give the posterior distribution. • Prior is the Wilson distribution • p(J) = (1/Σ) exp( - J/ Σ) if J ≥ 0 (Acentric) • p(J) = 0 if J < 0 • p(J) = 1/(2πΣJ) exp( - J / 2Σ) if J ≥ 0(Centric) • p(J) = 0 if J < 0 • J is intensity, Σ is the mean intensity in the resolution shell S French and K S Wilson ActaCryst. A34, 517 (1978)

  4. K S Wilson A J C Wilson

  5. Output intensity vs Input intensity (acentric) I/σ J/σ – σ/Σ

  6. Output Amplitude vs Input Intensity (acentric) F/σ½ J/σ – σ/Σ

  7. FUTURE WORK • Twinning (H test initially) • Anisotropy (Clipper/Popov and Bourenkov) • Multiple data sets

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