# 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.

167 questions
Filter by
Sorted by
Tagged with
10 views

### How to sample one sample from the posterior such that the sample lies within a certain credible interval using pymc?

I am working with pymc where i am trying to sample solely one sample from a posterior that has been truncated to a certain credible interval. I want the posterior to have been truncated such that all ...
• 31
20 views

### May we choose the confidence interval's width or credible interval'swidth based on a loss-function or cross-validation?

May we choose the confidence interval or credible interval based on an empirical risk loss-function? I think we blindly generate the width intervals without any optimization or rely on some ...
24 views

### Closed form credible region/marginal credible interval for Gaussian distribution

Suppose we have a multivariate Gaussian distribution $X \sim \mathcal{N}(\mu,\Sigma)$ where $\mu=(\mu_1,\mu_2,\dots,\mu_n) \in \mathbb{R}^n$ (the posterior of a conjugate Gaussian prior perhaps). Is ...
• 11
1 vote
61 views

### How to calculate Bayesian marginal credible interval?

I have a Bayesian model that I've fit using Stan, and I'm trying to figure out the best way to calculate the correct credible interval that I am interested in. The model is a hierarchical GLM with a ...
• 292
36 views

### 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. ...
• 23
33 views

### 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, ...
• 53
58 views

### 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'...
19 views

### 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 ...
• 337
117 views

### 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 ...
• 2,090
19 views

### 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 ...
• 101
1 vote
44 views

### 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 ...
• 61
76 views

### 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 ...
• 53
387 views

### 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 ...
41 views

### 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. ...
• 93
1 vote
37 views

### 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 ...
• 326
84 views

### 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 ...
• 1,193
1 vote
96 views

### 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 ...
17 views

### 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 ...
181 views

### 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 ...
• 83
38 views

### 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, ...
45 views

### 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
189 views

### 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, ...
476 views

• 9,559
1 vote
67 views

### 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 ...
• 57
41 views

### 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 ...
• 97
1 vote
18 views

### 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 ...
• 35.7k
62 views

### 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%...
• 73
1 vote
32 views

### 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 ...
• 51
159 views

### 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} = \...
67 views

### 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 ...