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The English Reverend Thomas Bayes was a Presbyterian minister who primarily wrote on spiritual matters, but who was also known to dabble in mathematics—including an interest in probability.
This interest led to the production of an essay, which was published posthumously, entitled “An Essay Towards Solving a Problem in the Doctrine of Chances.”
Within this work he shared a solution to what at the time was called the problem of inverse probability, but which today is more typically referred to as the probability distribution of an unobserved variable, which refers to how one might figure out the likelihood of something when we don’t have perfect knowledge of it.
This is a useful problem to solve because we seldom have perfect knowledge of anything: there are so many possible variables influencing every single decision we might make in real life that it’s unlikely that we would be capable of computing every single possible influence informing a given decision.
The solution presented—which was a special case of what later became known as Bayes’ Theorem—isn’t perfect in the sense that it tells us with absolute precision everything we might want to know about the likelihood of something happening.
What it does provide us is a reliable means of assessing probability within the confines of imperfect knowledge; how likely something might be in the real world.
Thus, we’re able to ascertain how likely it is that an individual will be hit by a car sometime in the next year, and how likely it is that the same person will live to be 80-years-old. We can refine our search-and-rescue parameters when someone has gone missing, and we can figure out the reproduction number of a new disease, even before we know much else about it.
We can also use an extension of this concept called Bayesian Inference to update our existing beliefs, often called our priors, in a probabilistically optimal way.
If I believe fire will burn me if I touch it, but I see an illusion that I don’t realize is an illusion of a man touching fire and it not hurting him, there’s a chance that I might update my priors based on what seems to be new, valid information.
I might, in other words, come to believe that in at least some circumstances I can touch fire and not be burned—which would, in most cases at least, be a non-ideal change to my functional knowledge base.
In other cases, however, such changes to our beliefs are desirable.
If I’m a doctor who believes, based on all of my education and experience, that diseases are caused by miasmas—by bad air—but new research comes along that indicates disease is instead caused by tiny creatures called viruses and bacteria, this could lead to a challenging but valuable update to my mental library of information that then informs all of my future actions and assumptions for the better.
Bayesian Inference provides us with math that helps us figure out which situation is which: when we’re accepting as fact information that is likely to lead to negative future outcomes, and when we’re making prudent updates to our collection of assumption-informing data.
The mathematical formula for Bayesian Inference is not typically applied in personal and interpersonal situations: the literal version of this concept is generally most useful within scientific, engineering, philosophical, legal, and similar fields.
A rough version of Bayesian Inference can serve as a useful heuristic, though, when we’re trying to figure out when to update our priors and when to discard new data as inferior to what we’ve already got.
The heuristic version of this concept might be defined in this way: it’s important to remain humble in our ability to know anything, and it’s generally prudent to think in terms of probability ranges rather than certainties—to think of what we know as the current, most-likely possibilities, rather than as absolute, unchangeable truths.
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