Statistical confidence intervals are almost always misinterpreted. Consider the following statement.
"The prevalence of the disease P has a 95% confidence interval of 1% <= P <= 5%."
This is commonly taken to imply that there’s a 95% chance that the true prevalence is between 1% and 5%.
This isn’t the case.
Confidence intervals represent uncertainty about the interval, rather than the parameter of interest.
The correct interpretation of the confidence interval defined above is that if we collect many samples from the population and calculate confidence intervals from them, 95% of those confidence intervals will contain the true value of P.
In Bayesian statistics we generally calculate credible intervals which are compatible with the intuitive interpretation.
