In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution.[1] The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals in frequentist statistics,[2] although they differ on a philosophical basis:[3] Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value. Also, Bayesian credible intervals use (and indeed, require) knowledge of the situation-specific prior distribution, while the frequentist confidence intervals do not.
Credence is a statistical term that expresses how much a person believes that a proposition is true
Why this matters:
It seems like a lot of questions EAs are interested in involves subjective Bayesian probabilities. A lot of people misuse the frequentist term “confidence interval” for these purposes (to be fair, this isn’t just a problem with EAs/rationalists, I’ve seen scientists make this mistake too, akin to how the p-value is commonly misunderstood). I think it’s helpful to use the right statistical jargon so we can more easily engage with the statistical literature, and with statisticians.
Thank you for writing this! I once failed a job interview because what I learned from the EA community as a ‘confidence interval’ was actually a credible interval. Pretty embarrassing.
Credible Interval:
Credence:
Why this matters:
It seems like a lot of questions EAs are interested in involves subjective Bayesian probabilities. A lot of people misuse the frequentist term “confidence interval” for these purposes (to be fair, this isn’t just a problem with EAs/rationalists, I’ve seen scientists make this mistake too, akin to how the p-value is commonly misunderstood). I think it’s helpful to use the right statistical jargon so we can more easily engage with the statistical literature, and with statisticians.
Thank you for writing this! I once failed a job interview because what I learned from the EA community as a ‘confidence interval’ was actually a credible interval. Pretty embarrassing.
Wow that’s an awfully specific way to fail a job interview! But I’m glad you’ve learned something from it, at least?