vstatmp_engl

Index 397

121.Upper limit for a Poisson rate with background

122.Upper limit for a Poisson rate with uncertainty in background and acceptance

Chapter 9

123.Deconvolution of a blurred picture

124.Deconvolution by fitting the true event locations

Chapter 10

125.Bias and inconsistency of a test

126.The p-value and the probability of a hypothesis

127.Comparison of di erent tests for background under an exponential distribution

128.χ2 comparison for a two-dimensional histogram

129.Likelihood ratio test for a Poisson count

130.Designed test: three region test

131.GOF test of a two-dimensional sample

132.Comparison of two samples

133.Significance test: signal over background, distribution of the likelihood ratio statistic

134.Example 133 continued

Chapter 11

135.Simple empirical relations

136.Search for common properties

137.Two-class classification, SPAM mails

138.Multiclass classification, pattern recognition

139.Curse of dimensionality

140.Principal component analysis

141.Calorimeters in particle physics

Chapter 12

142.PDE of a background distribution and signal fit

143.Bootstrap evaluation of the accuracy of the estimated mean value of a distribution

144.Error of mean distance of stochastically distributed points in a square

145.Acceptance of weighted events

146.Two-sample test with a decision tree

Appendix

147.E ciencies of di erent estimates of the location parameter of a Gaussian [77]

148.E ciency of small sample MLEs

149.Parameter uncertainty for background contaminated signals

398Index

150.Coverage: performance of magnets

151.Bias in the measurements for a mass determination

152.Inference with known prior

153.Bias introduced by a prior

154.Comparing predictions with strongly di ering accuracies: Earth quake

155.Fitting a mean value in presence of outliers