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Statistical Image Modelling and Particle Physics Comments on talk by D.M. Titterington

Statistical Image Modelling and Particle Physics Comments on talk by D.M. Titterington. Glen Cowan Royal Holloway, University of London PHYSTAT05 Oxford, 15 September 2005. Glen Cowan RHUL Physics. PHYSTAT05. Unfolding for particle physicists.

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Statistical Image Modelling and Particle Physics Comments on talk by D.M. Titterington

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  1. Statistical Image Modelling and Particle PhysicsComments on talk by D.M. Titterington Glen Cowan Royal Holloway, University of London PHYSTAT05 Oxford, 15 September 2005 Glen Cowan RHUL Physics PHYSTAT05

  2. Unfolding for particle physicists V. Blobel, Unfolding Methods in High Energy Physics, DESY-84-118; also CERN 85-02. G. Zech, Comparing statistical data to Monte Carlo simulation-- parameter fitting and unfolding, DESY 95-113 (1995). R. Barlow, SLUO Lectures on Numerical Methods in HEP (Lecture 9: Unfolding), 2000. G. Cowan, Statistical Data Analysis (Ch. 11), OUP, 1998. N. Bissantz, Regularized inversion methods and error bounds for general statistical inverse problems, PHYSTAT05. N. Gagunashvili, Unfolding with system identification, PHYSTAT05. + now DMT’s PHYSTAT paper and its 2 pages of refs. Glen Cowan RHUL Physics PHYSTAT05

  3. Connections with and differences from HEP Image reco: many pixels, Gaussian noise noisy image true scene HEP: (often) data are numbers of events, ~102 bins ‘true histogram’ measured histogram expectation value of data response matrix Glen Cowan RHUL Physics PHYSTAT05

  4. Connections with and differences from HEP In image reco, point spread function (response matrix) is essentially a property of the measuring device: In HEP this is often almost true, but resolution in a variable of interest x can depend on the value of some other variable y. E.g. energy resolution might be better if particles often have large angles w.r.t. beam →H has model dependence. This model dependence is one source of systematic uncertainty in the unfolded distribution; also modeling of measurement device itself difficult (probably worse problem...). Also technical difficulties in determining H: need lots of MC, smoothing(?) Glen Cowan RHUL Physics PHYSTAT05

  5. Connections with and differences from HEP Image reco: if new feature visible, it worked. HEP: need not only unfolded distribution but full covariance matrix and estimate of systematic biases. Image reco: Bayesian method using priors motivated by statistical physics (Ising model). HEP: could we write down an appropriate prior? Glen Cowan RHUL Physics PHYSTAT05

  6. Bias vs. variance Unregularized solution unbiased, huge variance. But (at least in Poisson case), the variance is at as small as you can get for zero bias (Minimum Variance Bound). →to reduce catastrophic variance you must put up with some bias. Bias vs. variance trade-off determined by regularization parameter. DMT mentions several recipes not yet explored in HEP, e.g., (generalized) cross-validation, Bayesian prescription Glen Cowan RHUL Physics PHYSTAT05

  7. Iterative methods In HEP iterative technology used e.g. G. D’Agostini NIM A362 (1995) 487. DMT describes many variations on this theme -- we need to read these references! Glen Cowan RHUL Physics PHYSTAT05

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