BlueFin Best Linear Unbiased Estimate Fisher Information aNalysis Andrea Valassi (IT-SDC) based on the work done with Roberto Chierici TOPLHCWG meeting on Statistical Combination Tools 11 th November 2013

A. Valassi – BlueFin2  The code was prepared over the last ~20 months to test various ideas we got while working on our paper  “Information and treatment of unknown correlations in the combination of measurements using the BLUE method” (  Why are BLUE weights negative? Are correlations overestimated? What is the most “conservative” choice of correlations? How much “information” does each measurement contribute (what is its “relative importance”)?  The C++ code has changed enormously in time as new ideas appeared and old “new” ideas were abandoned  Started off by migrating to C++ the Fortran code used for LEPEWWG  Focus was initially on splitting up information contributions among measurements (e.g. via integrals) – now moved out of the way  SVN ( is now a cleaned up version that only contains the ideas that made it into the paperhttps://svnweb.cern.ch/trac/bluefin  Initially born as a small private test (largely out of curiosity in my free time), not as user-oriented software to be supported Why BlueFin? – the original goals

11 th November 2013A. Valassi – BlueFin3  One executable: bluefin [options] [ /].bfin  Builds an output pdf report from an input text file  For N-parameter combinations: print BLUE results  In addition, for 1-parameter combinations: information analysis (information weights and derivatives)  A small library of C++ classes for this executable:  BlueFish – one N-parameter combination  Exact BLUE (central value, weights, error split-up) via matrix algebra  BlueFish1Obs – more specific 1-parameter case  Plus some helpers: InfoAnalyzer, InfoMinimizer …  Some examples (internally used as tests)  LEP (W branching ratio, σ WW ), TOP (m t ), ad-hoc examples BlueFin – what does it do?

11 th November 2013A. Valassi – BlueFin4 Example – input file

11 th November 2013A. Valassi – BlueFin5 Example – “nominal” correlations Information derivatives w.r.t. correlations (only for 1-observable combinations) Central value weights <0 indicate a “high-correlation regime” Correlations with the highest derivative (RED in the table) are those most responsible for this effect

11 th November 2013A. Valassi – BlueFin6 Example – modified correlations Details for each “modified correlation” scenario are in the following pages of the BlueFin report -Modified input covariances (full and partial) -Detailed BLUE results, CVW, MIW, IIW -Details about minimization, onionization….

11 th November 2013A. Valassi – BlueFin7  The fact that this was a small test that grew larger over time can be seen by many limitations:  Matrix algebra is done via Boost and (hence?) is slow  ROOT only appeared later to add minimizations  Still many “assertion” exceptions to check hypotheses (“is this sum the same as this other sum?”) – precision limited  Random use of triangular vs. symmetric matrices  No CppUnit – tests done by reproducing full real examples  External dependencies assume CERN’s CVMFS or AFS  All these points could easily be addressed if needed Internals – and some limitations

11 th November 2013A. Valassi – BlueFin8  Executable exists and is very easy to use  Write an input text file and you get lots of useful information  Automatic creation of tables in a pdf report via pdflatex  Software tested on some real life examples  Used for regression testing (require reproducible results)  Examples also represent simple doc for users Internals – some of the good points

11 th November 2013A. Valassi – BlueFin9  BLUE results are Unbiased as long as the individual measurements are Unbiased  But it is true that we traditionally treat our systematic biases as randomly (and Gaussian!) distributed variables  We could think of treating random (e.g. statistical) errors and unknown systematic biases in different ways?  In my opinion, understanding inter-measurement correlations for those systematic biases would remain (and be even more!) essential in that case  And splitting the total errors into fine-grained correlated sources of uncertainty remains the first step Beyond BLUE and Gaussian errors? (1)

11 th November 2013A. Valassi – BlueFin10  Two different problems are often being discussed  1. Why are central value weights in BLUE negative? That is to say, are correlations being (“conservatively”) overestimated?  2. Should we move beyond BLUE and Gaussian approximations eventually?  Addressing the second issue will probably involve a more complex (hence more opaque) procedure  This may “hide” the first issue, but we should not ignore it!  BLUE weights (especially the ugly negative ones) may disappear, but correlations may still remain overestimated!  IMO, the analysis provided by BlueFin is useful even if one should move beyond BLUE and Gaussian errors!… Beyond BLUE and Gaussian errors? (2)