In one of our projects, we encountered this dilemma where we had to nitpick on (the probability of) co-occurrence of a pair of events and correlation between the pair of events. Here is my attempt at disambiguating between the two. Looking forward to any pokes at loopholes in my argument. Consider two events e1 and e2 that have a temporal signature. For instance, they could be login events of two users on a computer system across time. Let us also assume that time is organized as discrete units of constant duration each (say one hour). We want to now compare the login behaviour of e1 and e2 over time. We need to find out whether e1 and e2 are taking place independently or are they correlated. Do they tend to occur together (i.e. co-occur) or do they take place independent of one another? This is where terminologies are freely used and things start getting a bit confusing. So to clear the confusion, we need to define our terms more precisely. Co-occurrence is simply the probability that
(Acknowledgment: This post has inputs from Sanket of First principles fame.) When teaching about formal axiomatic systems, I'm usually asked a question something like, "But, how do you find the axioms in the first place?" What are axioms, you ask? To take a few steps back, reasoning processes based on logic and deduction are set in an "axiomatic" context. Axioms are the ground truths, based on which we set out to prove or refute theorems within the system. For example, "Given any two points, there can be only one line that passes through both of them" is an axiom of Eucledian geometry. When proving theorems within an axiomatic system, we don't question the truth of the axioms themselves. As long as the set of axioms are consistent among themselves (i.e. don't contradict one another) it is fine. Axioms are either self-evident or well-known truths, or somethings that are assumed to be true for the context. But then, the main question becomes ver