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Very often in text-books the comparison of Bayesian vs. Classical Statistics are presented upfront in a very abstract way. For example, in the current book I'm studying there's the following postulates of both school of thoughts:

"Within the field of statistics there are two prominent schools of thought, with op­posing views: the Bayesian and the classical (also called frequentist). Their fundamental difference relates to the nature of the unknown models or variables.

In the Bayesian view they are treated as random variables with known distributions. In the classical view, they are treated as deterministic quantities that happen to be unknown."

But as a beginner student in this field there's a lack of 'substance', of something you can 'feel'. So would I like to know, if somebody has a real world example of both cases. Like the same example, but seen from both perspectives to help understanding 'what's going on'. Thanks!

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A good way to understand how these two perspectives differ is to look at how they approach the problem of confidence intervals. The question What's the difference between a confidence interval and a credible interval? has some excellent discussion on this, including examples where both approaches are taken and shown to give different answers.

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