Please explain what the two approaches are? The similarity and the difference between them. If possible examples as well

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The frequentist approach uses objective experience about how frequently an event is likely to occur, such as coin tosses, or the probability of a defective product on an assembly line. As the experience increases, the observed frequency is increasingly predictable (or its statistical properties are). Since it is based on observations, there is no room for opinions or gut feel.

This approach doesn’t work for many situations, however. Until one has accumulated sufficient experience from repeatable experiments, what number is to be assigned? Now, one may legitimately ask, what is the hurry to assign a number at all? Just wait it out until we have sufficient experience. But that does not help the insurance industry, for example. When SpaceX puts out a new rocket, what should it be insured for? The quote depends on how likely one “feels” it is going to crash, since there is no experience of it being launched.The insurer would have to go with a gut feel, based on the opinion of experts in the industry and come up with a number. Also, they need a way to tweak the number as more and more data emerges. Gamblers and insurers have always used Bayesian methods.

In the limit case (with sufficient experience or repeated randomised trials), the two should converge.

The frequentist approach to statistics views the probability of some event as equal to frequency of that event given unlimited trials. That is, the probability of a coin toss producing heads is 0.5, because that’s what the frequency of heads converges to as you make more and more tosses.

The Bayesian approach considers probability to represent our degree of belief in some event that can be updated as we improve our understanding of that event with new data. For example, we consider the probability of a coin toss producing heads equal to 0.5 because we believe that the coin is fairly symmetrical and that the person tossing the coin does not possess the level of muscle control necessary to influence the results of the toss. If we learn that the coin isn’t symmetrical, or that the tossing is done by a robot with extremely precise motions, then we would conclude that the probability is something else, based on our understanding.