Prediction and Probability 2

Hi there

First, let’s being with the last thing I said in my previous post, "How to deal with the uncertainty associated with the outputs of our model?”. In general sense, all models usually have some coefficients which they might be meaningful and representative of a fact (like the slope in linear regression models) and some of them may not. Let’s get back to my Gompertz function again:

Y(X)=a*exp(-b*exp(-c*X)) .

Think about it....

Let's assume 30 paired set of data for your X and Y have been measured and in order to fit this Gompertz function a software has been used to determine the model's coefficients (a, b and c).

But what does the whole process mean?

It means that from your huge population of Y and X, you have taken a sample 30 and then you have implicitly assumed that it represent the whole population of X and Y. But does it? Actually, I'm not suggesting to take 10^n sample to be able to capture the variation of the whole population and I know how difficult, costly and even time consuming is data measurement.

I'm just trying to encourage you to think about the underlying assumptions of your models and how valid are they?

Basically, by using the procedure explained earlier for developing a simple nonlinear regression model like Gompertz, the uncertainty rooted into the heterogeneity of sample, sample size and quality of measurement has been never incorporated into the model.

Ok, that's enough.

I would like to put a solution forward :). I’ll be suggesting a method which it lets you to define and also determine how likely is it to get a specific value as an output from your model. By this way you know how much is the probability (or how reliable is) of happening a specific output and I believe it is one of the coolest thing I have ever learned. So that's why am I calling this as the prediction with probability (I'm just kidding. it's just a made up word ;)),

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