Many words have already been said about confidence intervals for estimating a parameter in bayes and frequency. There are dozens of explanations, but none of them shows "on fingers" how the mechanisms for creating these intervals differ . So let's also try to explain it to you so that you will never again be embarrassed at mentioning them.
The frequency analysis, as you probably heard, there is one problem: few people understand how to correctly interpret the classical frequency confidence intervals ( confidence intervals ). Therefore, they are often confused with Bayesian ( credible intervals ).
The information below contains the nuts and bolts of constructing both confidence intervals (which for some reason are not described in books and forums), as well as the disadvantages of using these methods.
Frequency
In statistics textbooks, they say: "You have a point estimate for some parameter. Now plug it into the formula for the confidence interval. Here is your interval. Trust it with a probability of 0.95, whatever that means." Before discovering the existence of Bayesian inference, there were no questions, right? And now, in order to understand the difference in thinking, you have to understand in a new way and in frequency.
I propose to consider an example of estimating an unknown parameter of an abstract distribution. Suppose we have some arbitrary distribution with some variance σ 2 and expectation μ . At μ has a specific value (denoted in the figure), but imagine that we do not know where it is. Our task is to estimate what μ is equal to .
According to the central limit theorem, we take a sample of size n from the general population and calculate its arithmetic mean X̄ . If this operation is repeated many times, the values of X̄ will have a normal distribution N (μ, σ 2 / n)... Let's plot this on a graph.
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: , , X̄ ± 2 * std.
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, μ2 , , X̄ ( ). μ, likelihood priors. , , μ = μ2. μ.
, μ, , 95% (HPDI) . .
, X̄, , . , , , .
So, we closed the topic of confidence intervals for continuous values . I sincerely hope that these conclusions are infallible, but I am open to any criticism.
If you are also interested in discrete intervals , I recommend that you carefully read the cookie example described in the answer on the StackExchange forum.