I got the posterior distribution of a parameter from Bayesian analysis. I want to express it as confidence interval. If I plot the empirical cumulative distribution function of the parameter and obtain the 95% interval, will it represent the 95% confidence interval?
No, an X% confidence interval is one where the true value falls within it X% of the time. So a Bayesian credible region can represent a confidence interval only when the frequency coverage matches. It doesn't have to, because the prior can shift the profiles. Best way to check is via simulations.