There are two main perspectives in statistical inference. They are Baysianism and frequentism. So what are they? Let’s understand them using a coin-tossing example. It goes like this. What is the probability of getting a head if I toss a coin?
Bayesian first assumes, then update
Well, the answer depends on whom you ask! If you ask a Baysian, she will start the following way: a coin has two sides – a head and a tail. Since I don’t know whether the coin is fair or biased, I assume in favour of the former. In that case, the probability is (1/2), and then, depending on what happens, I may update my belief!
Frequentist first counts, then believe
You ask the same question to the frequentist, and she will hesitate to assume but will ask you to do the tossing a hundred times, count them and then estimate!
How can one event has two different chances?
The toss just happened, but the outcome is hidden from your sight. The question is repeated: what is the probability that it is a head? The Bayesian would still say it is (1/2). The frequentist’s perspective is different. The coin is already landed, and there is no more probability: it has to be either a head or a tail. If it is a head, the answer is 100%, but if it is a tail, the answer is 0%!
Who is right?
If you recall my old posts, I have used Bayesian mostly in calculations but frequentist for explaining things. One classic example is the weather forecast. The easiest way we can understand a 40% probable rain tomorrow is if I tell you that when such weather conditions happened in the past 100 occasions, it rained in 40 of them. And you are happy with the explanation. But in my weather model, I may have used 0.4 as a parameter and depending on what happened tomorrow (actually, it rained), I may have updated my model like a true Bayesian.
