Prediction and Probability

Have ever thought about it? I feel like, it’s one of those cool topics to think about? I tried to keep the terms “Prediction” and “Probability” as general as it’s possible to make very broad inference about them. You may probably ask yourself, “What’s he talking about, stochastics models are the best example of the integration of probability and any kind of prediction”. But, how many of you have ever used stochastics models or have any idea how these models work.

As we hear prediction, it somehow implies that at some level there is uncertainty associated with that estimation. But, we never incorporate these level of uncertainty into our deterministic models. Most of the models that we use daily as part of our research projects such as empirical, statistical (regression) and even numerical models, they are deterministic. They just spit out a single value as their prediction for a process or event. But, it was just two lines above that we agreed that every single prediction has some level of deviation from the “TRUE” value. So what can we do about it?

I would like to bring a more detailed example. There is function called Gompertz that it can describe the growth of different things such as crop, microbial community or even tumor growth. Here is how this model look like:

y(t)=a*exp(-b*exp(-ct))

Just assume for your special case a is equal to 1, b is equal to 2 and c is equal to 3. Then by passing different values of (t) to this function, it gives you a single value corresponds to that input. But is it all that makes you happy?

Think about it …..

In my next post I will be bringing some ideas to deal with this situation.