Observable sensitivities – prof-sensitivities¶

A crucial decision at the beginning of every tuning effort is to decide which observables should be included in the tune, i.e. included in the goodness of fit function that is optimized with prof-tune. To assist you with this decision prof-sensitivities calculates the sensitivity of a data bin to the model parameters. However, this does not replace a good knowlegde of the model that is tuned. Rather, the sensitivity can help you to identify parameters that are less important and might be excluded in a tune and to identify observables that can be used to constrain parameters. To make the calculation of the sensitivity fast the polynomial interpolation of the MC response is used for this.

The --datadir DATADIR and related options are used as normal to specify the reference data, MC runs, and interpolation objects: see the path options page.

prof-sensitivities can create color map plots and 2D plots visualizing the extremal sensitivity. The type of plot can be chosen with --plotmode. The accepted values are described below under Plot modes. The sensitivity definition can be selected with --definition. The different definitions are discussed under Sensitivity definitions. The location where the plot files are created can be given by -o OUTDIR.

prof-sensitivities expects that the observables for which the sensitivities are calculated are specified in the file given by --weights WEIGHTS. The file WEIGHTS can be in the usual format used to specify observable weights or a simple list of observables, one per line. The location of the interpolation coefficient cache files (created with prof-interpolate) and optionally the reference data must be given by the data-location options, e.g. --datadir or --ipoldir and --refdir.

The order of the polynomial used for interpolation can be specified by --ipol-method and the run combination is taken to be the first one in the file given by -R RUNSFILE.

Example¶

Create extremal sensitivities derived from sampling along a cross in parameter space using the default definition and plot style:

prof-sensitivities --datadir my/data/ -R myruncombinations --weights sensitivity.observables

The above will produce one plot for each observable in sensitivity.observables in the default output directory sensitivities.

Plot modes¶

Basically two different types of plots can be produced: color maps and 2D plots showing only the extremal sensitivity for each parameter. The color maps show the sensitivity for each parameter and observable in a separate plot, i.e. one ends up with $N = N_\mathrm{obs} \cdot N_\mathrm{params}$ plots. When the sensitivity of observable O on parameter P1 is calculated the remaining parameters are not varied, i.e. the sensitivity is calculated along a cross in parameter space:

p_2  ^
     |
     |           x  ==> Sensitivity for parameter p_2
     |           "
     |           x
     |           "
     |           x
     |           "
     |  =x=x=x=x=o=x=x=x=x=x=x=x   ==> Sensitivity for parameter p_1
     |           "
     |           x
     |           "
     |           x
     |
     +----------------------------->
                                  p_1

The center of the cross (o in the above) can be set using --paramsfile or --paramsvector. By default the center of the parameter hyper cube used for interpolation is used.

The accepted color map plot modes are:

colormap: Create a color map for each observable-parameter combination. Each plot has its own scale for the z-axis data.
colormaplim: Same as colormap. But all plots have the same scale for the z-axis data.
colormapobslim: Same as colormap. But all plots for the same observable have the same scale for the z-axis data.

The accepted extremal plot modes are:

extremal: Produce one plot per observable. Only the extremal sensitivity value found on axes of the cross is plotted.
extrandom: Same as extremal. But instead of calculating the sensitivities along the axes of a cross, the sensitivity is calculated at points sampled randomly from the parameter space and only the extremal value for each parameter is kepts. The range from which the points are sampled can be specified with --paramsrange. It defaults to the range of the anchor points used for the interpolation.

Sensitivity definitions¶

Several different ways how to calculate the sensitivity are implemented which are more or less robust for some borderline cases. The sensitivity definition should take into account that both parameters and the bin values have different scales. Consider, for example, two parameters with physical meaningful ranges of

$0.1 < p_1 < 0.4 , \quad 1.0 < p_2 < 10.0 ,$

and two bins, $b_1$ and $b_2$ , where the first is typically of order 10 and the other of order 1000.

If, now, changing $p_1$ or $p_2$ by 0.1 changes $b_1$ by 1 unit we say that $b_1$ is more sensitive to $p_2$ than to $p_1$ because to gain a change of 1 unit in $b_1$ we have to move our $p_1$ value by ~30% but the $p_2$ value only ~1% of the expected range. If, on the other hand, changing $p_2$ by 0.1 changes $b_1$ and $b_2$ by 1 unit we say that $b_1$ is more sensitive to $p_2$ than $b_2$ because change of a bin with content of 1000 ( $b_2$ ) by 1 is not as exciting as the same change in a bin with a content of 10 ( $b_1$ ).

So what we are looking for is something like a relative derivative as

$S_i = \frac{\partial \ln MC(p)}{\partial \ln p_i} = \frac{\partial MC(p)/MC(p)}{\partial p_i/p_i}$

i.e. to norm the differential by the values they are taken at.

However, this is not working for either $MC = 0$ or $p_i = 0$ . To work around this, we use a slighly modified definition:

$S_i = \frac{\partial MC(p)}{|MC(p_0)| + \epsilon \, w_{MC}} \frac{|p_{0,i}| + \epsilon \, w_{p_i}}{\partial p_i}$

where $p_0$ is assumed to be a typical set of parameter values (set by --paramsfile, --paramsvector or the center of --paramsrange) and the $\epsilon$ terms are introduced to work around the borderline cases $MC, p_i = 0$ . $w_{p_i}$ corresponds to 80% of the original sampling range and $w_{MC}$ is constructed from this.

Todo

List the available sensitivity definition.

Command-line options¶

The --datadir DATADIR and related options are used as normal to specify the reference data, MC runs, and interpolation objects: see the path options page.

Output/Plot style¶

--plotmode PLOTMODE¶: The type of plots to produce, see Plot modes. [default: extremal]

--definition DEFINITION¶: The sensitivity definition to use, see Sensitivity definitions.

--table TABLEFILE¶: Create a LaTeX table stub in TABLEFILE for all one-bin observables in extremal plot modes. By default no such file is created.

--splines, --no-splines¶: Do/do not connect data points with splines in the extremal plot modes. Default is to draw the splines.

--legend, --no-legend¶: Put/don’t put a legend on every plot in extremal plot modes. Default is to draw a legend.

--logy¶: Use a logarithmic scale for the sensitivity axis in extremal plot modes. Default is to use a linear scale.

--make-plots¶: Create output files suitable for make-plots when producing color map plots. Default is to use matplotlib for plotting.

Input¶

--paramsfile PARAMETERFILE, --pf PARAMETERFILE¶: File with parameter values used as center of the parameter cross.

--paramsvector PARAMETERSTRING, --pv PARAMETERSTRING¶: String specifying the parameter values used as center of the parameter cross. E.g. PAR1=42.0,PAR2=0.23.

--paramsrange RANGEFILE, --pr RANGEFILE¶: File with parameter sampling range for extrandom plot method.

-R RUNSFILE, --runsfile RUNSFILE, --runcombs RUNSFILE¶: A file with the run combination that is used for the interpolation. Only the first run combination in this file is used. [default: runcombs.dat]

--ipol-method IPOLMETHOD¶: The interpolation method. At the moment the order of the polynomial: quadratic or cubic. [default: quadratic]

--weights WEIGHTS, --obsfile WEIGHTS¶: A file listing the observables and their weights which are used in the GoF.

Observable sensitivities – prof-sensitivities¶

Example¶

Plot modes¶

Sensitivity definitions¶

Command-line options¶

Output/Plot style¶

Input¶

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Observable sensitivities – prof-sensitivities¶

Example¶

Plot modes¶

Sensitivity definitions¶

Command-line options¶

Output/Plot style¶

Input¶

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