From: Roger Hälg <rhaelg_at_phys.ethz.ch>

Date: Thu, 17 Feb 2011 23:56:10 +0100

Date: Thu, 17 Feb 2011 23:56:10 +0100

Dear Alberto

Thank you for your illustrative explanations. I have a further question.

FLUKA is a microscopic analogue Monte Carlo code with the exception of

the handling of low energy neutrons. Does this group-algorithm change

anything concerning statistical errors when averaging over neighbouring

bins? Or in other cases when biasing is used?

Regards,

Roger Hälg

On Thu, 2011-02-17 at 23:35 +0100, Alberto Fasso' wrote:

*> Roger,
*

*>
*

*> in addition to Mario's answer, I would like to stress that the
*

*> table in the FLUKA course material (taken from an old MCNP manual
*

*> - the new one is more politically correct and doesn't say "garbage" but
*

*> "useless" :-) refers to errors of "integral" quantities, such as
*

*> the average fluence or dose in a region. For "differential" quantities
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*> such as binnings, or spectra, large errors don't mean necessarily
*

*> useless results. This is because neighbor bins, or energy intervals,
*

*> are correlated: what is counted in one bin is not counted in the next
*

*> one, and vice versa. The calculation of the standard deviation of a given
*

*> bin is based on the reproducibility from run to run of that bin only, and does
*

*> not take into account the bins close to it.
*

*> In practice, the best way to judge the quality of binned results is to plot
*

*> them as a function of one coordinate. If the points look nicely and smoothly
*

*> "aligned", without wild fluctuations, the results are most often acceptable.
*

*> Bad statistics normally shows up as large, irregular fluctuations. And since
*

*> "what is counted in one bin is not counted in the next one", the fluctuations
*

*> become smaller if you average neighbor bins as discussed with Mario.
*

*>
*

*> One more remark on this subject: often binning results are plotted in the
*

*> form of color plots. On most color plots, the ratio of the plotted quantity
*

*> from one color to the next in the color log scale is of the order of 2 or 3.
*

*> For this reason, even with errors larger than 50% the plot can look
*

*> good (the errors are smaller than the color resolution) and the boundaries
*

*> between colors are smooth and not ragged. So, even large errors don't make the
*

*> results completely useless (but one should use the single bin numerical values:
*

*> the plot allows just a decent global view which is often all that is required).
*

*>
*

*> Alberto
*

*>
*

*> On Thu, 17 Feb 2011, rhaelg_at_phys.ethz.ch wrote:
*

*>
*

*> > 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
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*> > error.
*

*> > To be more specific, let me describe an example. I simulated a proton
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*> > beam impinging a water phantom to score neutron dose. I used a pretty
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*> > small bin size. To improve the statistical error, I used the symmetry of
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*> > the irradiation field and of the phantom to average bins perpendicular
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*> > to the beam but keeping the full resolution in beam direction. The
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*> > 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
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*> > group algorithm is used and the calculation is no more microscopic
*

*> > analogue?
*

*> >
*

*> > Thanks again very much for your help!
*

*> >
*

*> > Regards,
*

*> >
*

*> > Roger H?lg
*

*> >
*

*> > 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
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*> >> 3D matrix generated by USRBIN.
*

*> >> But the plot can only be made in 2D, so you need to choose what kind of
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*> >> 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 Fri Feb 18 2011 - 10:44:03 CET

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