Goodness-of-fit tests for unbinned maximum likelihood - Physics ...

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$1 Ch. 22 â Reflection and Refraction of Light 22.1 The ... - Physics$

Compound hypothesis: K 1 distributionsome examplesObservations• still resemble exponential decay• "decay constant" varies w fitted function, parameter (notsimple as c 2 /ndf) BUT approx. consistent for N=10->1000!=> consistency over changes, in parameter, N.• very amenable to determination via toy MC9PHYSTAT2003,9/8/03
Treatment of multidimensional dataTo be developed• K 1 in 1-d, no ordering of data -> amenable to multi-d?Look at 2-d• Data on unit circle -> 2-d toroid in 4-d: what iscorresponding vector algebra?• More obvious: projections - extend Fourier formalismk 1 =0 or k 2 =0 corresponds to projection onto f 2 or f 1(k 1 ,k 2 )= (1,1), (1,–1), 1), etc. " other axesDevelop statistic from orthogonal projections?PHYSTAT2003,9/8/0310
Page 2 and 3: BELLEWhy we are interestedBelle & o
Page 6 and 7: BELLEAn analytic study of the energ
Page 8: BELLECorrelation between fitted par
Page 13 and 14: Flat null hypothesisMC - generatedf
Page 15 and 16: Compound hypotheses: rejection powe
Page 17: Compound hypothesis: data-parameter

Goodness-of-fit tests for unbinned maximum likelihood - Physics ...

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