Ramas (Applied Biomathematics)

- Constructor Software

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RAMAS Constructor is software for the Windows operating system that implements several techniques for selecting and parameterizing an uncertain number from sparse or imprecise knowledge. It can be used to construct probability distributions, probability boxes (p-boxes), or Dempster-Shafer structures (DSSs).  Using p-boxes and DSSs, the uncertainty inherent in the data can be rigorously represented and propagated through calculations.  Quantitatively incorporating uncertainty in this way provides an automatic and exhaustive sensitivity analysis of the importance of uncertainty in the inputs.

Constructor enhances transparency and reproducibility which increases the credibility of an analysis by encouraging the clear and complete documentation of all sources of information used and the choices and judgements made in constructing each input.  Constructor provides a self-documenting interface which prompts the user for documentation and description of source material and for explanation and justification of each decision made in the derivation of an input.  Units are checked and unit conversions are performed automatically to pre-empt errors.  Color coding highlights potential problems and directs the user to incompletely documented data sources or unjustified decisions.

Constructor provides eight ways to use the information you have to specify an uncertain number. To specify your number you may enter:

  • Data
  • Qualitative shape information
  • Named distribution shape
  • Moments
  • Order statistics
  • Coverages
  • Density
  • Graphical information

Constructor collates the information you enter to specify a probability distribution, a probability box, or a random sets (Dempster-Shafer) structure. Click on the type of information you wish to use in the list above or scroll down this page for more details about how to tell Constructor what you know and what Constructor does with that knowledge.

Constructor makes it easy to document the sources of your knowledge and the reasoning behind your decisions.  Follow this link to see how.

Use data to specify an uncertain number

Clicking the 'Data' tab opens a page where data may be entered to constrain an input distribution.  Bothintervals and precise points may be entered and p-boxes or Dempster-Shafer structures specified.  Intervals are preferable in cases where points are uncertain due to, for example, measurement error.  For interval data, enter the minimum in the column labeled 'Left' and the maximum in the column labeled 'Right'. For point observations, enter the same number in the left and right columns.  Check the 'Specify weights' checkbox to enter weights.  The minimum and maximum may be the extremes of the data entered or may be extremes derived from other considerations. The radio boxes present four methods for using the data to specify the uncertain number: stochastic mixture, sample rule, Saw-Yang-Mo, and Kolmogorov-Smirnov confidence limits.

Use qualitative shape information to specify an uncertain number

Selecting the 'Shape' tab opens a page where distribution shape information may be entered to constrain the input distribution.  You may not know the exact distribution shape, but you may know, for example, that it is surely symmetric.  In this case, Constructor will constrain the set of possible input distributions to those where the mean equals the median.  Similarly, if you know that the distribution is surely positive, only distributions with minimums greater than or equal to zero will be considered.  Nine other qualitative parameters, including unimodality, concavity, convexity, increasing or decreasing hazard, discreteness, continuousness, and integer or constant valued, may be specifed to constrain the input distribution.  

Use a named distribution shape to specify an uncertain number

In some cases, you may know that the input is distributed according to a named distribution family.  Forty such families are implemented in Constructor and may be selected from the dropdown menu labeled 'Distribution shape' on the 'Shape' page.  When you select a distribution family, boxes will appear in which you can enter the parameter values necessary to specify the named distribution.  Distribution and paramter choices are documented and explained by right-clicking on them to bring up the justification editor.  If uncertain numbers, e.g. intervals, are used to parameterize a named distribution, the result will be a p-box or DSS which bounds all of the distributions of the selected family that could result from every possible realization of the parameters.

Use moments to specify an uncertain number

Clicking on the 'Parameters' tab opens a page where moments may be entered to specify constraints on an input distribution.  Moments may be entered as precisely known points or as intervals.  Constructor uses combinations of known moments, whether certain or uncertain in nature, to constrain the limits of the input distribution.  The moments you enter will be colored yellow until you document and explain them.  Right-click on a moment to bring up the justification editor.

Use order statistics to specify an uncertain number

Clicking on the 'Percentiles' tab opens a page where order statistics may be entered to specify constraints on an input distribution.  Order statistics may be entered as precisely known points or as intervals.  Constructor uses known percentiles, whether certain or uncertain in nature, to constrain the limits of the input distribution.  Precise knowledge of an order statistic provides a powerful constraint on the input distribution because the set of possible inputs is reduced to only those which pass through that single point.  The order statistics you enter will be colored yellow until you document and explain them.  Right-click on an order statistic to bring up thejustification editor.

Use coverages to specify an uncertain number

When you select the 'Coverages' tab, a page appears that allows you to specify intervals which 'cover' the input distribution with known probability.  Constructor uses these intervals and their corresponding probabilities to constrain the limits of the input distribution.  An interval is entered by typing its minimum in the 'Left bound' box and its maximum in the 'Right bound' box, selecting either 'exactly', 'no less than', or 'no greater than' from the 'covers' drop down menu, and entering a probability in the 'Probability' entry field.  

Probabilities entered must be between zero and one in each row, however the probabilities across rows need not add to one.  

Use density to specify an uncertain number

When you select the 'Density' tab, a page where you may specify limits on a probability density function (pdf) is displayed.  Double-clicking anywhere in the probability density graph will bring up a little spreadsheet where you can enter x-values and corresponding densities for both the 'bubble' and the 'cap'. The cap is the upper bound on the density at any particular point on the x-axis.  The bubble is the lower bound on the density.  Between the bubble and the cap is the area from which the uncertain pdf may be drawn.  Double-clicking anywhere on the spreadsheet reverts to the pdf graph. Any point on the pdf graph may be manipulated by clicking and dragging it to the desired location. You can zoom in on any part of the image by clicking and dragging a box from upper right to lower left around an area of interest.  To un-zoom, click and drag from lower right to upper left.

Use graphical information to specify an uncertain number

Selecting the 'Graph' tab brings up a page where you can manipulate the graphs produced on other pages.  The figure below shows the graph tab after data was entered in the 'Data' tab.  You may use your mouse to drag the left and right bounds to adjust the input distribution as necessary.  Note that you can zoom in on any part of the image by clicking and dragging a box from upper right to lower left around an area of interest.  To un-zoom, click and drag from lower right to upper left.

How to enter documentation and justification for your uncertain number

Right-clicking anywhere you entered information will bring up a justification editor customized for the kind of information you entered.  Two examples are shown below.  The first is the justification editor you see when you right-click on the data entry area of the 'Data' page.  The second is the justification editor you see when you right-click anywhere you specified the minimum of the input distribution.  In most cases, your entered information will be colored yellow until the first five or six boxes in the justification editor are filled.

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