Neutron groups and statistical error

From: Roger Hälg <>
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?


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
> 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, 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
> > 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 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
> >> 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: [] On Behalf Of Roger Haelg
> >> Sent: Tuesday, February 15, 2011 6:01 AM
> >> To:
> >> 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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