The bayesian Method begins with a strange introduction to “Bayesian thinking” :
Unlike more traditional statistical inference, Bayesian inference preserves uncertainty.
In the Bayesian world view, probability is interpreted as the degree to which we believe something will happen.
In other words, it shows our confidence that it will happen.
Why is there a little “idealism” of subjectivity and confidence here?
In contrast to Bayesian, the frequentist believes that:
The probability is the probability that an event will occur over a long period of time.
Let’s say you keep flipping a standard coin, you have a 50% chance of getting heads.
But history doesn’t have that much data on the Scorpion disaster.
What to do?
Thus, Bayesian interpretation of probability as confidence in the occurrence of events, that is,
Probability is an overview of ideas.
Just because probability is subjective doesn’t mean bayesian is a bunch of subjective guys.
Instead, they are always ready to update their views.
Bayesian believers accept new information (evidence) that contradicts their beliefs, even when it is irritating and insulting to their intelligence.
As Keynes is said to have said, “When the facts change, so do my ideas. What about you?”
But they are not simply fickle. Instead of discarding old beliefs because of new information, they put all the information together through an uncomplicated formula.
The Bayesian approach concludes:
Even with the new evidence, we have not completely abandoned our original belief.
But we recalibrate our beliefs to make them more consistent with current evidence (that is, the evidence makes us more confident about certain outcomes).
By introducing a priori uncertainty, we are actually allowing our initial beliefs to be wrong.
After looking at data, evidence, or other information, we constantly update our belief to make it less wrong.
The value of these ideas is more valuable than “simple” Bayesian computing.
Bayes’ method, in my opinion, is a kind of “brain lever”.