MPGSA questions regarding plot visualizations and log-distributed sampling

Hello,

I have two questions regarding MPGSA analyses:

1. When analyzing many independent variables, I cannot visualize the subplots (see attached) when the plot() and histogram() methods are run. Is it possible to break these into individual figures?
2. It appears the x axes are in linear scale, although I sampled the parameters using loguniform distributions. Is it possible to display the x axes in log scale when sampling is done on log scale?
3. Also, along the lines of (2), can I confirm whether the logarithmic distribution of the sampling is taken into account when the K-S calculations are performed?

Thank you,

Abed

Answer 1

[Florian Augustin]

Hello Abed,

You can use the name-value pair Parameters in the plot or histogram methods to selectively visualize GSA results. You can either specify the input parameters as a numeric index or via their names. Looking at the screenshot you attached, you could select kdA and kdB as follows:

plot(mpgsaResults, "Parameters", [3, 4]);
% or
plot(mpgsaResults, "Parameters", ["kdA", "kdB"]);

In the current version of Matlab (R2021b), there is no name-value pair in the GSA plot methods to change the axes scale. But here is a little script you could use/tweak to manually change the scale:

function figHandle = plotInXLogScale(mpgsaResults, varargin)
    % Create plot
    figHandle = plot(mpgsaResults, varargin{:});
    % Get axes handles from figure
    axes = findobj(figHandle, "Type", "Axes");
    % Change x-scale of axes to log-scale
    for i = 1:numel(axes)
        axes(i).XScale = "log";
    end
end

I am not sure I understand the third question, but you can inspect the parameter samples on the MPGSA results object, e.g. by plotting them in a histogram:

% Plot parameter samples for input parameter kdA:
histogram(results.ParameterSamples.("kdA"));

Let me know if this doesn't answer your question.

Hope this helps.

Best,

-Florian

[Abed Alnaif]

Hi Florian,

Regarding the first question, thanks, I missed this in the documentation but this is exactly what I'm looking for.

Regarding the second question, I think this is a good solution for the plot() method. I'm not sure if it will work with the histogram() method.

To clarify the third question: I'm not very familiar with the K-S Test, but I have a high-level understanding that it's designed to detect differences between CDFs. My concern is that a difference between two CDFs may be apparent when the x axis is in log scale, but not when it is in linear scale. I'm not sure if this makes sense?

Thank you,

Abed

[Florian Augustin]

Hi Abed,

The simple change of scale of the axes also works for the histogram plots. However, this does not change, the bin boundaries, which will remain equidistant on a linear scale. Changing the binning boundaries to be equidistant on a log-scale is not supported.

To get equidistant bins on a log-scale, you have to create custom histogram plots:

%% Setup
%  -----
% Index of classifier in the order specified in sbiompgsa:
classIdx = 1;  % choose 1 if you only have one classifier
% Index of parameter in the order specified in sbiompgsa:
paramIdx = 3;  % this would select kdA
% Create bounds of bins in log scale:
binEdges = logspace(2, 4, 10); % example: 10 equidistant bounds on log-scale between 10^2 and 10^4.

%% Plot
%  ----
% Parameter samples
samples = mpgsaResults.ParameterSamples{:, paramIdx};

% Index of samples that support classifier:
supportSamples = mpgsaResults.SupportHypothesis{:, classIdx};
% Index of valid samples (for which simulation did not fail):
validSamples   = mpgsaResults.SimulationInfo.ValidSample;

% Plot:
figure(1); clf;
histogram(samples(supportSamples & validSamples), "BinEdges", binEdges, "Normalization", "probability");
hold("on");
histogram(samples(~supportSamples & validSamples), "BinEdges", binEdges, "Normalization", "probability");

To visualize the values of the K-S statistic, I would recommend using bar plots. There the numeric values are are more apparent than in the eCDF plot plots. You can also access the raw numeric values as a table:

mpgsaResults.KolmogorovSmirnovStatistics

Best,

Florian