# RE: FLAIR projections and statistical error

From: <rhaelg_at_phys.ethz.ch>
Date: Thu, 17 Feb 2011 15:26:13 +0100

Dear Mario

Thank you for your detailed explanation. The part of the projections is
now clear to me, but I still have questions concerning the statistical
error.
To be more specific, let me describe an example. I simulated a proton
beam impinging a water phantom to score neutron dose. I used a pretty
small bin size. To improve the statistical error, I used the symmetry of
the irradiation field and of the phantom to average bins perpendicular
to the beam but keeping the full resolution in beam direction. The
statistical error for my binning with the original bin size is,
depending on the location inside the phantom, quite high. According to
the table in the FLUKA course material with a statistical error of about
50%, the result can be within a "factor of a few" to "garbage".
After averaging over multiple bins perpendicular to the beam as
described above, the statistical error drops far below 10% and should be
reliable according to the table.

My question is now, is this spatial averaging acceptable to reduce the
statistical error and can the result be stated as reliable? Or is the
error on the original bin size still dominant?
If yes, is this also true in case of low energy neutrons, where the
group algorithm is used and the calculation is no more microscopic
analogue?

Thanks again very much for your help!

Regards,

Roger Hälg

On Tue, 2011-02-15 at 14:34 -0800, Santana, Mario wrote:
> Roger,
>
> Let's take as an example a 2D plot. Usually you will want to plot a
> 3D matrix generated by USRBIN.
> But the plot can only be made in 2D, so you need to choose what kind of
> view you want (e.g. elevation, plain, cross section ~ X, Y, Z depending on
> your reference frame). If you project the matrix on the y-z plane (X axis),
> you will be plotting a {y, z} mesh in which each point {y_j, z_k} is the
> average value of all the layers with the same {y_j, z_k} but different x_i
> (x_1, x_2...). If you specify limits for your x axis, then FLAIR will only take
> into account all the layers between your specified x range. The associated
> error, for any {y_j, z_k} bin is obtained in FLAIR by calculating the
> relative error of the sum of bins and dividing by the square root of the
> numberof terms. In FLAIR you can actually select the 'error' box to plot the
> associated relative errors. If you do so, remember to set the normalization
> factor to 1 and to use a scale ranging from 0 (or close) to 100.
>
> Anyway, in most practical cases, if your plot looks smooth (isolines are
> well defined, no big traces, nor 'random' fluctuations in neighboring values)
> most likely your statistical error will be acceptable. Of course, this
> depends on the scale range that you use, so use good judgment.
>
> Mario
>
>
> -----Original Message-----
> From: owner-fluka-discuss_at_mi.infn.it [mailto:owner-fluka-discuss_at_mi.infn.it] On Behalf Of Roger Haelg
> Sent: Tuesday, February 15, 2011 6:01 AM
> To: fluka-discuss_at_fluka.org
> Subject: FLAIR projections and statistical error
>
> Dear FLUKA and FLAIR experts
>
> Could anyone explain to me what the "projection& limits" for data plots
> (1d and 2d) in FLAIR exactly do with the data for plotting? The manual
> does not explain this.
>
> And what happens to the statistical error in this case? The manual says:
> "WARNING errors will be underestimated, since it treats all bin values
> as uncorrelated."
> How can I estimate the error when using this projections and limits for
> several bins? Are there different cases to be differentiated?
>
> In the FLUKA course materials there is a table listing the statistical
> errors and the usefulness of the results. Is this always related to the
> statistical errors of the individual bin or is there a way to estimate
> the error using projections and averaging?
>
> Thank you very much for your help!
>
> Regards,
>
> Roger Haelg
>
Received on Thu Feb 17 2011 - 23:00:18 CET

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