# Tagged Questions

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### Confidence intervals and central estimates for a functional of an estimated function with uncertain parameters

I've got a problem that is leading me to dip my toes into Bayesian stats, and I've got a question about confidence (or, I suppose, credible) intervals: Say you want to know how $X$ maps to $y$. You ...
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### How do I interpret the credibility interval in a Bayesian Regularized Regression?

A penalized regression provides biased estimates of the regression coefficients (bias-variance trade-off principle). Therefore, standard errors and confidence intervals are regarded as not very ...
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### Prediction and 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 ...
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118 views

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### Bayesian and frequentist optimization and intervals

I realize the methodology pursued by the Frequentist and Bayesian camps generally differ. However, one method of estimation that they do share is optimization of a certain function: Frequentists ...
1answer
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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 ...
2answers
1k views

### Quantile intervals vs. highest posterior density intervals

I am reading a bit about Bayesian analysis, but I cannot understand the difference between the classic quantiles and the Highest Posterior Density Intervals. What is the difference between the two? I ...
2answers
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### Nonparametric credible intervals

I have a small (n ≈ 15) IID sample from a continuous distribution that I have no reason to believe (a priori or a posteriori) belongs to a familiar parametric family. I do know a priori that the ...
4answers
221 views

### How can I use credibility intervals in Bayesian logistic regression?

I'm using Gibbs sampling to learn the distributions of coefficients for a multinomial logistic regression model. At the end, I end up using the mean values of distributions of coefficients, and the ...
7answers
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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 the difference between confidence intervals and credible intervals were the correct ones. How you would ...