Changes between Version 3 and Version 4 of MatrixElement


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Timestamp:
04/12/12 11:57:14 (7 years ago)
Author:
md987
Comment:

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  • MatrixElement

    v3 v4  
    99The best estimate of the parameter $\alpha$ is obtained through a maximisation of the likelihood. It is common practice to minimize $-ln(L(\alpha))$ with respect to $\alpha$, $-ln (L)=-\sum_{i=1}^{N} ln(\bar{P}(x_i;\alpha)) + N \int \bar{P}(x,\alpha)dx$
    1010
    11 In general, the probability that an event is accepted depends on the characteristics of the measured event, and not on the process that produced it. The measured probability density $\bar{P}(x,\alpha)$ can be related to the produced probability density $P(x,\alpha)$: $\bar{P}(x,\alpha){{{
    12 Acc(x) P(x,\alpha)$ where $ Acc(x)$ is the detector acceptance, which depends only on $ x $. So the quantity that we have to minimize is $-ln (\tilde{L})
    13 }}}-\sum_{i=1}^{N} ln(P(x_i;\alpha)) + N \int Acc(x) P(x,\alpha)dx$ where the term $-\sum_{i=1}^N ln(Acc(x_i))$ has been omitted since it does not depend on $\alpha$.
     11In general, the probability that an event is accepted depends on the characteristics of the measured event, and not on the process that produced it. The measured probability density $\bar{P}(x,\alpha)$ can be related to the produced probability density $P(x,\alpha)$: $\bar{P}(x,\alpha){{{Acc(x) P(x,\alpha)$ where $ Acc(x)$ is the detector acceptance, which depends only on $ x $. So the quantity that we have to minimize is $-ln (\tilde{L})}}}-\sum_{i=1}^{N} ln(P(x_i;\alpha)) + N \int Acc(x) P(x,\alpha)dx$ where the term $-\sum_{i=1}^N ln(Acc(x_i))$ has been omitted since it does not depend on $\alpha$.
    1412
    1513== Definition of the Weight ==