Difference between a parameter and a variable

[Lilly]

Hello,

I have started my preparations for subject CT4 for the next exam sitting. I have gone through the first chapter. However, being a statistician myself I have been getting confused over the usage of the terms "parameter" and "variable" in the chapter. As far as I know, in a model, a variable represents the characteristics of the real world system or process and its values vary with each measurement. It can also be a random variable. But a parameter is a constant that gives the size of the relationship between the variables. So a parameter comes only after a variable has been defined. And one may also have plain constants that are not attached to any variable known as autonomous items in the model.

In the first chapter, I have come across several instances where the term parameter has been used when the author wants to say variable. The following are the some cases:

1) On page 56, "The possible errors associated with the model, or parameter used not being a perfect representation of the real world situation being modelled".

2) On page 62, "Input parameters need to be chosen, possibly by statistical analysis of past data. Sensitivity ananlysis of the dependence of the output on these parameters can be carried out".

3) On page 64, Exam style question -- "The value of the current assets is under our control so we can change this to make sure that the 0.5% requirement is met. Other parameters for eg. future long term interest rates, future inflation rates are not under our control. So we will need to test how sensitive our answers are to the changes in these parameter values".

Pl do tell me if what I have stated above is correct. I like to be specific and hence this clarification.

Looking forward to your help.

With regards,
Lilly

 

[Louisa]

Hi Lilly -
I think the terms variable and parameter are used quite carefully in the notes. Whether technically correctly or not I wouldn't know.

They use variable for something that varies inside the specific model we're looking at, whether randomly or deterministically. Parameter is used for numbers that are put into the model as a fixed input (but could be changed externally, e.g. sensitivity testing, scenario testing).

So the use in the below examples seems consistent.
The example on p64 is interesting. The figures for long term interest rates in the model may be treated as parameters for a particular purpose - i.e. treated as inputs not modelled. However, if we want to test how real life responds to different values of these parameters we'd have to wait until the combination of parameters we're interested in "happened to" turn up, which could take a while. But if we have a model we can just plug in the values and see what happens.

Could you give an example of what you mean by a "plain constant" that you would not call a parameter?

Louisa