Monte Carlo Simulation Tutorial - Uncertain Functions and Statistics

Uncertain Functions and Statistics

We’ve now defined the uncertain variables in our risk analysis model.  Anything calculated from these uncertain variables is an uncertain function, but usually we’re interested only in specific results such as Net Profit at cell B11. When we “turn on” Interactive Simulation, B11 will effectively hold an array of values, each one calculated from different values sampled for B4, B5, B6 and B7.

What would we like to know about the array of values for Net Profit at cell B11?  The simplest summary result is the average (or mean) Net Profit.  Note that this will be the true average of Net Profit across 1,000 or more scenarios or trials -- not a single calculation from average values of the inputs.  With cell B11 highlighted, we click the Statistics button on the Risk Solver Ribbon.  A dropdown gallery shows us the available statistics functions, which we can "drag and drop" into a worksheet cell.

When we click the Mean button, a small “balloon” like the one below appears and follows the mouse pointer as we move to a worksheet cell, in this case B12. When we click to select the cell, the formula =PsiMean(B11) appears in the cell.

When we define a summary statistic, such as PsiMean(B11), we’ve implicitly designated cell B11 as an uncertain function.  Risk Solver will keep track of the full range of trial values for B11 during a simulation, and will display frequency and sensitivity charts, statistics and percentiles for it on demand. As noted above, in principle anything calculated from the uncertain variables is an “uncertain function” -- but to save time and memory, Risk Solver keeps track of trial values only for the formula cells that we designate.  There are several ways (besides using a statistic such as PsiMean) to designate a cell as an uncertain function.

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