# 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.

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### How is highest posterior density interval estimated in this code snippet?

I found the following (Julia) implementation for estimating the highest posterior density interval from a posterior sample (link). Below, I turn it into pseudocode for simplicity. ...
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### SAS Bayesian 95% credible intervals for proportions or crosstabs [closed]

I am trying to find SAS code for figuring 95% credible intervals as relates to differences two proportions or a contingency table. I see there is proc MCMC but the examples I see are 1 proportion, and ...
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### Deriving Bayesian Credible Intervals for AUC using R brms

I am trying to estimate the posterior distribution for the AUC of a predictive biomarker using R brms. However, whenever I calculate the AUC using the posterior distribution of the model parameters, ...
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### Wide prediction intervals for short time series: how to fix that?

I have very small time series data(24 points) for sales for different-different regions. I need to build Range Forecast (Confidence/Credible Intervals) for sales around it for every region. I tried FB'...
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### Estimate quantile coverage

I have implemented, say, a (Bayesian) quantile regression model and I want to assess it by comparing the predicted conditional quantile interval between $Q_1$ and $Q_3$ with the true one (in a ...
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### How to fix hypothesis testing: MBF versus "directional correctness"

A common misinterpretation of a p-value is that it represents the probability of a false positive in the context of hypothesis testing. Here a "positive" means rejecting the null. There are ...
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### Comparing Star Ratings

Data Illustration NOTE: I do not have a stats background. I'm pretty sure I'll use some terminology incorrectly. I have come across several approaches via Python/SQL that I would like to confirm as ...
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### What is the relationship between model uncertianty and model parameter count?

I'm looking for references, information and/or existing theory behind the relationship between the uncertainty in a given model vs its complexity/parameter count. The situation I have in mind is using ...
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### Using the terminology "Bayesian confidence interval" in place of "Bayesian credible interval."

In Peter Hoff's "A first course in Bayesian statistical methods," he states: "Most authors refer to intervals of high probability as 'credible intervals' as opposed to confidence ...
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### How to find 95% credible interval of a posterior predictive distribution?

I obtained a posterior predictive with 1,000 samples using MCMC, and I need to quantify the 95% credible intervals. I know that the difference between confidence intervals and credible intervals. One ...
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### How can I combine credible intervals when there are differences in slope terms from interactions?

Let's say I run this model with a continuous by categorical interaction where Species has 3 levels. ...
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### Why do we trust credibility intervals to contain the true parameter?

I understand confidence intervals and to what extent they can be trusted (and why). However, I’m not so sure how to motivate why I should trust credibility intervals except insofar as they can also ...
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### D&D - Confidence Interval for enemy armor class

In dungeons and dragons, characters and monsters have two properties called Attack Bonus($AB \, \in \, \mathbb{Z}$) and Armor Class($AC \, \in \, \mathbb{N}$). Let $AB_c$ be the character attack bonus ...
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### Practical consequences of wrong interpretation of confidence intervals

Can you give me a simple (but preferably common) example (or R/Python simulation) of what are practical consequences of wrong interpretation of frequentist confidence intervals? Especially when they ...
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### False Discovery Rate From Posterior Samples of Bayesian Models

This is likely a naive question but here goes. There are a number of papers on Bayesian FDR (Efron/Efron and Tibshirani) etc. All of these models seem to assume that the score(p value or z values, or ...
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### mcmc vs the bootstrap

What is more accurate, the mcmc derive 95% credible interval or the bootstrap derived 95% confidence interval? Can this be proved mathematically? the emphasis of the Bayesian approach is that one is ...
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### Bayesian estimation of mutual information for continuous variables

I am looking for references that derive a Bayesian estimator for mutual information in the case of continuous data. My understanding is that this has been explored for discrete (e.g. Hutter, 2002, ...
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### Statistical conclusions from incompatible measurement results

I assume that the following situation is not uncommon in scientific practice: Two research groups analyse two samples. The reported results concern the same physical quantity at the same location ...
1 vote
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### Showing calibration of Bayesian credible intervals

I'd like to try and understand how one can prove that a particular strategy for assessing correctness of computational methods for Bayesian inference is sound. For a number $M$ of simulations, ...
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### True parameter in relation to credible interval

I know that in the frequentist approach, the confidence interval contains the true parameter $\theta$ with some minimum probability (e.g. 95%); while in the bayesian approach, the credible interval ...
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### Transitivity of Bayesian inference

For more context about this question, please see my other question. Note that I'm a beginner in Bayesian methods. To recall, I'm trying to estimate the ratio of execution times from two different ...
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### Calculating the (colloquial) likelihood of a result

A project that I am working on wants to use two factors to determine risk. First is an assessment by a subject matter expert (SME) on how much damage a calculated result would cause. Second is a ...
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### Credible Interval on 2 Random Variables

Assuming we have two random variables, $A$ and $B$, each are assumed to follow a normal distribution with unknown mean and variance. A random sample has been drawn from each $A$ and $B$. How is the 99%...
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### Link functions and interpreting credible intervals

I am pretty new to statistics, and was trying to interpret credible intervals from a bayesian analysis I had preformed. Some of my models are glms, and so have a link function. I know that to ...
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### Bayesian Forecast: Credible interval with predicted regressors

I want to do a forecast of let's say orders with a Bayesian linear regression, where orders do not only depend on time but also on another regressor, let's say accounts at time t. orders_{t} = \...
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### Confidence intervals converging to credible intervals when Bootstraping?

As explained already by Rasmus, the Bayesian Bootstrap and the non-parametric Bootstrap "converge" when n is sufficiently large. But if taking the percentile interval in the Bayesian ...
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### Should I report credible intervals based on HDI or QI?

I have highly positively skewed outcome variable. I need to publish my results in an academic journal. tidybayes allows calculating credible intervals (CI) using median or mean with high density ...
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