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Work Easily with Stochastic Libraries,
SIPs and SLURPs
| As described by Dr. Sam Savage in
OR/MS Today, the simplest element of a coherent Stochastic
Library is a Stochastic Information Packet or SIP,
which is just a list of trial values for a single uncertain
variable. An example might be 1,000 sample values, in a specific
sequence, for the future price of oil at some point or interval
of time. In a Monte Carlo simulation, trials will be drawn from
the SIP in the order in which they were generated.
If the SIPs for several different uncertain
variables are generated as a group, in a manner that preserves
the statistical dependence between them, they may be combined
into a Stochastic Library Unit, Relationships Preserved,
or SLURP. A SLURP is a table of trial values, where
each column represents a specific uncertain variable, and each
row represents a distinct trial. The SLURP’s uncertain
variables may be dependent in ways not measured by
traditional correlation. But if a Monte Carlo
simulation draws trials in the specific order given by the
SLURP, this dependence will be reflected in the simulation model
results. |
Click on the example of SLURP
creation to see it full size. |
SLURPs in Excel
On an Excel spreadsheet, a SIP is naturally
represented by a column of cell values, and a SLURP is most
easily represented by a two-dimensional table of cell values. Of
course, SIPs and SLURPs could be stored in many other ways -- for
example, a SLURP could be a table in a relational or
multidimensional database, and the Excel Database Query
feature could be used to bring the data into a spreadsheet model.
Risk Solver provides two PSI Distribution
functions, PsiSip() and PsiSlurp(), that make it easy
to work with SIPs and SLURPs. PsiSip() takes one argument: a cell
range (usually a column) containing the trial values for one
uncertain variable. PsiSlurp() takes two arguments: a
two-dimensional cell range containing the SLURP data, and a column
index (starting from 1) for the uncertain variable whose trials
should be returned by the PsiSlurp() function.
Creating Stochastic Libraries
Of course, a Stochastic Library must first be
created before it can be used. In some cases, you may have a data
source from which you can draw SLURP data directly. For example, if
you are working with demographic data such as age, family size,
income, and taxes paid, you might be able to use a representative
sample directly as a SLURP. But in many cases, an expert
(perhaps like you) will have to select appropriate analytic
probability distributions and their parameters, determine
whether and how they should be correlated, and then generate
the trial data through a Monte Carlo process.
Risk Solver is a great tool for creating
Stochastic Libraries, as well as using them. It supports a wide
range of analytic distributions, shifting and truncation of
distributions, and rank order correlation of different
distributions. When you run a simulation, the trial data is
generated, and with the PsiData() function, you can easily
save the trial data in a column on the spreadsheet -- this will
create a SIP. Several PsiData() functions in adjacent
spreadsheet columns will create a SLURP.
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