Reducing the number of inputs (II)

As discussed in a previous post, a high number of inputs can cause a number of problems. Therefore, methods to reduce the number of inputs are of value. In the aforementioned post I mentioned that we can take advantage of the central limit theorem, and replace a large number added distributions with a single Normal distribution. However, we can sometimes change our perspective on the nature of the system we are considering, and reduce the number of input distributions that are required.

To demonstrate, consider the situation where we wish to analyze the risks associated with a new venture. An important part of this analysis would be the sales. This could be handled a number of ways, but let’s consider two basic ways. The first would be to specify a growth curve and use this to find the average sales for each period being considered (week, month, quarter or year, etc.), and then we would specify a standard deviation for each period and a distribution.  In this way each period is random and independent of the other, and a distribution is required for each. The second way would be to use a model (like the Bass model or a Gaussian CDF) to define the sales for each period, but this time we only allocate a distribution to each model parameter. This second way requires only around 2 or 3 distributions.

One might ask which approach (distributions for each period or distributions for the model parameters) is the most accurate. In fact, both are probably needed. However, using the approach that only allocates distributions to the small number of model parameters still provides a good representation of reality and requires less effort.  Thus, the general approach of developing a representative model of a situation and focusing upon allocating random variability to key parameters (as opposed to a larger number of intermediate variables) provides an avenue to generate a reliable and efficient model. Such a model makes an ideal first (and potentially final) attempt at analysis and optimization in the face of uncertainty.