10 - H1 - Desy

6.3 Classifier 81
step adjusts the free parameters of MVA to particular problem, the testing step checks
the quality of the trained MVA and the evaluation step is used during determination of
final results. Ideally, all three steps should be performed with statistically independent
samples. Due to high statistical demand of the MVA, the training and testing samples in
this analysis are single particle MC events with a single photons for signal (MC set XX in
table 2.5) and a single hadrons for background (MC sets XXI-XXX). This simplification
is possible since the MVA is purely based on the shower shapes and is insensitive to
the other activity in the detector 2 . In order to minimise possible bias though, for the
evaluation sample full prompt photon signal (MC sets I-II) and full background (MC set
XVI) simulation is used.
Table 6.2 summarises the number of MC events used in the MVA analysis. The training
sample consist of 60% randomly chosen events from the single particles MC samples. The
remaining 40% define the testing sample. The full MC simulation of prompt photon and
background events was used for the evaluation sample. Due to specific, highly demanding
usage of the evaluated discriminator, binned in multi-dimensional, extremely fine way
(see section 8.2.1), the signal evaluation sample exceed the testing sample by a factor of
roughly 75. The statistics for the background evaluating sample is relatively lower, due
to extremely low background selection ratio (of order 10 −5 ). Number of events listed in
the discussed table differ from tables 2.3−2.5 due to the selection criteria applied for the
training, testing and evaluating samples.
training testing
evaluating evaluating
(inclusive) (exclusive)
signal 221 ′ 709 147 ′ 456 16 ′ 981 ′ 407 11 ′ 309 ′ 443
background 246 ′ 512 164 ′ 453 72 ′ 354 58 ′ 445
Table 6.2: Number of signal and background events used for MVA.
6.3 Classifier 3
The MVA method chosen for this analysis is commonly known as maximum likelihood or
Naïve Bayes [117]. It builds a model out of probability density functions that reproduces
the input variables for signal and background. For a given event i, the combined signal
(background) probability p MV S(B) A (i) is obtained by multiplying the signal (background)
density probabilities p S(B) of all n var input variables.
2 Detailed study [66] shows that this assumption is not fully true. For a full MC event there is
a certain probability for a final state soft particle being counted in the selected cluster. This effect
produces statistically wider, more asymmetric and less compact clusters. In spite of this, single particle
approximation has been found to be good enough for the training and testing of MVA. This approach
produces a discriminator technically easier to obtain and though not anymore maximally optimal, still
correct, as long as evaluation sample correctly describes real cluster shapes.
3 All the classifiers methods were fully taken from the TMVA package [116].