Mawre Manipulations with Resolution Estimation of Value from Observation in Single Event

On the basis of resolution function K(x0; x) for some kinematical variable x we propose the method to estimate x̂ and + x ; x from observed x for a single event. We also propose the method to estimate parameters of resolution function from the set of test or Monte Carlo data fxtr i ; x i g. The last point to discuss is the correct choice of binning in x for smearing matrix used in the model of measurement after discretization of the problem. Numerical experiments were used for illustration. Estimation of value from observation in single event Resolution function K(x0; x) describes the probability to observe x = x0, when x = x was realized, where x is some one-dimensional continuous kinematical variable. For xed x = xF , K(x; xF ) is a probability density function (spread function, smearing function) Z 1 1 K(x0; xF )dx 0 = 1: In nite limits of integration mean all possible values of x0. In practice K(x0; x) is de ned on the limited rectangle x 2 [x min; x max], x0 2 [x min; x max], the last interval is derived fromK(x; x0) and the rst interval. From the experience we know K(x0; xF ) to be unimodal function, i.e. it has one maximum