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Questions tagged [credible-interval]

A credible interval is an interval in Bayesian statistics that includes the true value of a parameter with $(1−\alpha)\%$ probability. Credible intervals treat the interval as fixed and the parameter as random.

A credible interval is an interval that includes the true value of a parameter of interest with $(1−\alpha)\%$ probability. Credible intervals treat the interval as fixed and the parameter as random.

They are a Bayesian concept. The frequentist analog of a credible interval is a confidence interval. Although they are superficially similar, they are philosophically distinct.

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What's the difference between a confidence interval and a credible interval?

Joris and Srikant's exchange here got me wondering (again) if my internal explanations for the difference between confidence intervals and credible intervals were the correct ones. How you would explain the difference?
Matt Parker
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If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?

I'm very new to Bayesian statistics, and this may be a silly question. Nevertheless: Consider a credible interval with a prior that specifies a uniform distribution. For example, from 0 to 1, where 0 to 1 represents the full range of possible values…
pomodoro
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What is the connection between credible regions and Bayesian hypothesis tests?

In frequentist statistics, there is a close connection between confidence intervals and tests. Using inference about $\mu$ in the $\rm N(\mu,\sigma^2)$ distribution as an example, the $1-\alpha$ confidence interval $$\bar{x}\pm…
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What is a Highest Density Region (HDR)?

In statistical inference, problem 9.6b, a "Highest Density Region (HDR)" is mentioned. However, I didn't find the definition of this term in the book. One similar term is the Highest Posterior Density (HPD). But it doesn't fit in this context, since…
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How to summarize credible intervals for a medical audience

With Stan and frontend packages rstanarm or brms I can easily analyze data the Bayesian way as I did before with mixed-models such as lme. While I have most of the book and articles by Kruschke-Gelman-Wagenmakers-etc on my desk, these don't tell me…
Dieter Menne
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What is the decision-theoretic justification for Bayesian credible interval procedures?

(To see why I wrote this, check the comments below my answer to this question.) Type III errors and statistical decision theory Giving the right answer to the wrong question is sometimes called a Type III error. Statistical decision theory is a…
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How to correctly word a frequentist confidence interval

I am aware that there are many, many threads on this (e.g. this excellent thread). I may have missed it but I can't seem to find one that actually explains how to accurately report a frequentist confidence using the actual numbers contained in the…
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When does a confidence interval "make sense" but the corresponding credible interval does not?

It is often the case that a confidence interval with 95% coverage is very similar to a credible interval that contains 95% of the posterior density. This happens when the prior is uniform or near uniform in the latter case. Thus a confidence…
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How to find 95% credible interval?

I am trying to compute the 95% credible interval of the following posterior distribution. I could not find the function in R for it but is the approach below correct? x <- seq(0.4,12,0.4) px <- c(0,0, 0, 0, 0, 0, 0.0002, 0.0037, 0.018, 0.06, 0.22…
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Why would one use `random' confidence or credible intervals?

I was reading a paper recently that incorporated randomness in its confidence and credible intervals, and I was wondering if this is standard (and, if so, why it is a reasonable thing to do). To set notation, assume that our data is $x \in X$ and we…
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Examples of when confidence interval and credible interval coincide

In the wikipedia article on Credible Interval, it says: For the case of a single parameter and data that can be summarised in a single sufficient statistic, it can be shown that the credible interval and the confidence interval will…
Wayne
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Prediction interval = credible interval?

I am wondering if prediction interval and credible interval evaluate the same thing. For instance with a linear regression, when you estimate the prediction interval of a fitted values, you estimate the $(1-\alpha)\%$ limits of the interval in which…
droopy
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What does a confidence interval (vs. a credible interval) actually express?

Possible Duplicate: What, precisely, is a confidence interval? Yes, similar questions have been asked before, but many of the answers seem contradictory and don't address my issue. (Or my perception of the issue.) As mentioned many places, what…
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Interpretation of Bayesian 95% prediction interval

Assume the following bivariate regression model: $$ y_i = \beta x_i + u_i, $$ where $u_i$ is i.i.d $N(0, \sigma^2 = 9)$ for $i = 1,\ldots, n$. Assume a noninformative prior $p(\beta) \propto \text{constant}$, then it can be shown that the posterior…
TeTs
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Posterior variance vs variance of the posterior mean

This question is about the frequentist properties of Bayesian methods. Suppose we have data ${\bf y}$ generated from a distribution with a single parameter $\theta$, equipped with a prior $\pi(\theta)$. This leads to a posterior distribution…
knrumsey
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