Changes between Version 1 and Version 2 of MatrixElement

Timestamp:

Apr 6, 2012, 4:33:02 PM (12 years ago)

Author:

trac

Comment:

--

MatrixElement

@@ -7 +7 @@
 The likelihood for N events is defined as %\[ L(\alpha)=e^{-N \int \bar{P}(x,\alpha)dx} \prod_{i=1}^{N} \bar{P}(x_i;\alpha)\]%
 
-The 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 %$\alpha$%, %\[-ln (L)=-\sum_{i=1}^{N} ln(\bar{P}(x_i;\alpha)) + N \int \bar{P}(x,\alpha)dx\]%
+The 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 $\alpha$, %\[-ln (L)=-\sum_{i=1}^{N} ln(\bar{P}(x_i;\alpha)) + N \int \bar{P}(x,\alpha)dx\]%
 
-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 %$P(x,\alpha)$%: %\[\bar{P}(x,\alpha){{{Acc(x) P(x,\alpha)\]% 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 %$\alpha$%.
+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 %$P(x,\alpha)$%: %\[\bar{P}(x,\alpha){{{
+Acc(x) P(x,\alpha)\]% 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 $\alpha$.
 
 == Definition of the Weight ==
 
 The Matrix Element Method associates a weight to each experimental event %\[ P( x || \alpha)=\frac{1}{\sigma_{ \alpha}} \int d \phi( y) ||M_{ \alpha}||^2 ( y) dw_1 dw_2 f_1(w_1) f_2(w_2) W(x, y) \]% where
-   1. %$ x $% is the set of information describing the events in the detector (momenta,tag,...)
-   1. %$ \alpha $% describe a theoretical hyppothesis
-   1. %$\sigma_{ \alpha}$% is the cross section of this theoretical hyppothesis
-   1. %$M_{ \alpha}$% is the aplitude linked to this theoretical framework
-   1. %$f_i(w_i)$% is the parton distribution function associate to the initial parton
-   1. %$W(x, y)$% is the TransferFunction
+   1. $ x $ is the set of information describing the events in the detector (momenta,tag,...)
+   1. $ \alpha $ describe a theoretical hyppothesis
+   1. $\sigma_{ \alpha}$ is the cross section of this theoretical hyppothesis
+   1. $M_{ \alpha}$ is the aplitude linked to this theoretical framework
+   1. $f_i(w_i)$ is the parton distribution function associate to the initial parton
+   1. $W(x, y)$ is the TransferFunction
 
 == Computation of those elements ==
@@ -26 +28 @@
 
    1. TransferFunction
-   1. [:MadWeight:Computation of the Weight]
+   1. [wiki:MadWeight Computation of the Weight]
    1. AcceptanceTerm
 
@@ -48 +50 @@
 
 
+