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I’m going to pause here for you to take a breath and yell at your screen that it makes no sense. Of course, the number of faces is fixed, it’s a die! What Bayesian statistics quantifies with the distribution PPP is not how random the number of faces is, but how uncertain you are about it. This is the crucial difference and the whole reason why Bayesian statistics is so powerful. In frequentist approaches, uncertainty is often an afterthought, something you just tack on using some sample-to-population formula after the fact. Maybe if you feel fancy you use some bootstrapping method. And whatever interval you get from this is a confidence interval, it doesn’t tell you how likely the parameter is to be within, but how often the intervals constructed this way will contain the parameter. This is often a confusing point which makes confidence intervals a very misunderstood concept. In Bayesian statistics, on the other hand, the parameter is not a point but a distribution. The spread of that distribution already accounts for the uncertainty you have about the parameter, and the credible interval you get from it actually tells you how likely the parameter is to be within it.
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