I am working with software fro online analysis of PHOS/ALICE detector data

for the high level trigger (HLT).

Our detector response is shaped with a second order semi Gaussian

shaper with a rise time of ~4us. The signal is over sampled (That is errors are correlated). Im trying to find the ROOT packages to anylse my data, but the TMinuit

package, and the other packages in ROOT doesnt seems to taker into account correlated errors.

Is there any ROOT packages to handle the general case of the optimum fit

problem. That is, when errors might be correlated and the model for the

detetor response is nonlinear.

Fortunatly, one can most likely assume that the measurement correlation matrix

is Hermitan symetric.

I know one is doing something similar for track reconstruction where the scattering angle is is correalted with the spatial dispacement.

Regards

Per Thomas

Hi Per Thomas,

This statement is not correct ! Minuit is a general function minimizer . It

is up to the user to specify the correct objective function which can

among others contain terms for correlation between data points .

Eddy

Ok, I realize that have to be alittle bit more specific abouth my question.

May quastion is.

Is there any rootpackages available to handle the genral

Leas Mean Square (LMS) problem. Where the word "Mean"

implies that one is working with the least square fit based on the

knowledge of the statistical properties of the process.

(Same as Leas square fit in the special case when error are uncorrelated).

Per Thomas

Hi,

Let me try to write down what I think you are talking about :

You have a data set (x_ij, y_i, e_i) for i=1,N points

where there are j=1,M control variables and a covariance

structure so that

```
E(e_l e_k) = Cov_lk where E() means expectation value
```

You want to determine a function yFit(par,x) , assuming Gaussian

statistics … , this will lead to the following objective function:

```
(y-yFit)^T Cov (y-yFit)
```

Plug this expression in a function for Minuit and minimize wrt the

parameters par . The matrix /vector manipulations can be done

through TVectorD/TMatrixD …

Eddy

ps Googling “fitting auto-correlated time series”, you will find the

following interesting write-up:

` cran.r-project.org/doc/contrib/ Fox-Companion/appendix-timeseries-regression.pdf`