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My professor is comparing the frequentist confidence interval and the bayesian credible interval. He claims that a confidence interval is determined prior to observing the data, while the credible interval is determined after having observed the data.

I do not understand at all how a confidence interval could be determined prior to observing the data when a confidence interval is literally a function of the data. Is it possible that he meant something else by this wording?

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I think that what was meant is that the significance level of the frequentist confidence interval is set before you look at the data. If you specify p < 0.05 as your criterion, you determine 95% confidence intervals from the data and accept a significant result if the point estimate from the data is within that interval. The Bayesian credible interval is determined from the combination of the data and the assumed prior, so it too depends on a choice made before looking at the data.

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    $\begingroup$ But the significance level of the bayesian credibility interval is also set before we look at the data, no? $\endgroup$
    – David
    Commented Jan 23, 2020 at 14:47
  • $\begingroup$ @David I agree that a frequentist/prior versus Bayesian/posterior distinction is not very helpful. A Bayesian approach doesn't generally involve a hard true/false "significance level"; see this page for some discussion. Unlike frequentists, who assume there is one true set of parameter values so that a significance test is either true or false, a Bayesian approach tries to estimate the probability distribution of the parameter values. That probability distribution can then be used for further purposes, one of which might be a Bayesian test. $\endgroup$
    – EdM
    Commented Jan 23, 2020 at 15:54

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