Input and output variables of the URBAN model.

<p>Input and output variables of the URBAN model.</p

The URBAN model—sample results.

<p>The URBAN model—sample results.</p

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

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

Model is a force that changes data space.

<p>Model is a force that changes data space.</p

Model-Oriented simulation versus Data-Oriented simulation.

<p>Model-Oriented simulation versus Data-Oriented simulation.</p

Correlation of the three output variables.

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

Evolution of SA methodology.

<p>Evolution of SA methodology.</p