The Volatility of Data Space: Topology Oriented Sensitivity Analysis

<div><p>Despite the difference among specific methods, existing Sensitivity Analysis (SA) technologies are all value-based, that is, the uncertainties in the model input and output are quantified as changes of values. This paradigm provides only limited insight into the nature of models and the modeled systems. In addition to the value of data, a potentially richer information about the model lies in the topological difference between pre-model data space and post-model data space. This paper introduces an innovative SA method called Topology Oriented Sensitivity Analysis, which defines sensitivity as the volatility of data space. It extends SA into a deeper level that lies in the topology of data.</p></div

Two datasets with identical variance are different in nature.

<p>Two datasets with identical variance are different in nature.</p

The volatile outcome when the values of X1 and X2 are fixed to 3.0.

<p>The volatile outcome when the values of X1 and X2 are fixed to 3.0.</p

Correlation of the three output variables.

<p>Correlation of the three output variables.</p

Calculation results.

<p>Calculation results.</p

Evolution of SA methodology.

<p>Evolution of SA methodology.</p

Four types of topological measurements of data space.

<p>Four types of topological measurements of data space.</p

Centroid based TOSI’s.

<p>X1: preference for the store utility (α)</p><p>X2: preference for accessibility (β)</p><p>X3: dollar amount of purchase</p><p>X4: store operating cost per day.</p><p>Centroid based TOSI’s.</p

OAT sensitivity analysis on total driving distance.

<p>OAT sensitivity analysis on total driving distance.</p

Pearson correlation coefficient calculated for the three output variables.

<p>Pearson correlation coefficient calculated for the three output variables.</p