- #1
Daaavde
- 30
- 0
Hello everyone, I'm currently building the covariance matrix of a large dataset in order to calculate the Chi-Squared. The covariance matrix has this form:
\begin{bmatrix}
\sigma^2_{1, stat} + \sigma^2_{1, syst} & \rho_{12} \sigma_{1,syst} \sigma_{2, syst} & ... \\
\rho_{12} \sigma_{1,syst} \sigma_{2, syst} & \sigma^2_{2, stat} + \sigma^2_{2, syst} & ... \\
... & ... & ...
\end{bmatrix}
However, all my data points have asymmetrix uncertainties ([itex]d^{+ \sigma^+_n}_{- \sigma^-_n}[/itex]) where ([itex] \sigma^+_n \neq \sigma^-_n [/itex]).
How do I calculate the Chi-Squared in this case?
\begin{bmatrix}
\sigma^2_{1, stat} + \sigma^2_{1, syst} & \rho_{12} \sigma_{1,syst} \sigma_{2, syst} & ... \\
\rho_{12} \sigma_{1,syst} \sigma_{2, syst} & \sigma^2_{2, stat} + \sigma^2_{2, syst} & ... \\
... & ... & ...
\end{bmatrix}
However, all my data points have asymmetrix uncertainties ([itex]d^{+ \sigma^+_n}_{- \sigma^-_n}[/itex]) where ([itex] \sigma^+_n \neq \sigma^-_n [/itex]).
How do I calculate the Chi-Squared in this case?