RE: FLAIR projections and statistical error

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, 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
> 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: 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
>>
>
>
>

-- 
Alberto Fass