The Possibility of a Possibilistic Statistical Framework

A famous scientist from the Quantum Physics school of thought once said “asking the right question is more than halfway towards finding the answer.” Although it’s been years since I read this quote (which I may be paraphrasing, by the way), it still echoes a deep truth and helps guide my (non-academic) research in the data science and A.I. fields. So, I few weeks ago I put forward the question “what would a statistical framework framed around possibilities be like?”

At first glance, such a question may seem nonsensical since from an early age we’ve all be taught the core aspects of Stats and how it’s all about probabilities. There is no doubt that the probabilistic approach to modeling uncertainty has yielded a lot of fruits as the field grew, but all developments of Statistical methods were bound by the limitations of the assumptions made, mirrored by the various distributions used. In other words, if you want results with conventional Stats, you’ve got to use this or the other distribution and keep in mind that if the data you have doesn’t follow the distribution assumed, the results may not be reliable. What if the field of Stats was void of such restrictions by assuming a membership function instead of a distribution, to describe the data at hand?

I’m not going to describe in length where this rabbit hole leads, but suffice to say that the preliminary results of a framework based on this alternative approach exceeded my expectations. Also, there is no Stats process that I looked at which could not be replicated with the possibilistic approach. What’s more, since the possibilistic approach to data analytics is one of the oldest forms of A.I., it is sensible to say that such a statistical framework would be in essence AI-based, though not related to deep learning, since that’s a completely different approach to A.I. that has its own set of benefits. Nevertheless, I found that having a statistical framework that borrows an A.I. concept in its core, can provide an interesting way to bridge the gap between Stats-based data analytics and modern / A.I. based.

What’s even more interesting is that this can be a two-way street, with A.I. also being able to benefit from such a nexus between the two fields. After all, one of the biggest pain points of modern A.I. is the lack of transparency, something that’s a freebie when it comes to Stats modeling. So, an A.I. system that has elements of Stats at its core may indeed be a transparent one. However, this idea is still highly experimental, so it would be best to not discuss it further here.

Whatever the case, I have no doubt that the possibilistic approach to data has a lot of merit and hasn’t been explored enough. So, it is possible that it has a role to play in more modern data analytics systems. The question is, are you willing to accept this possibility?
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