# Questions tagged [credible-interval]

A credible interval is an interval in Bayesian statistics that includes the true value of a parameter with $100(1-\alpha)\%$ posterior probability. Credible intervals treat the interval as fixed and the parameter as random.

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### Is it possible to merge credible intervals from different Bayesian prediction models into a single estimate?

The situation Imagine an archaeological site, 10.0m deep. For my study, I construct an "age-profile" for this site, i.e., I produce a model of age as a function of depth. There are various ...
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### Simulate posterior from a linear mixed model with categorical and continuous variables and their interactions

Currently, I am working on a data set containing isotopic ratios. To understand differences in the ratios I am fitting a linear mixed model in R using the lme4 package. I am then using the arm package ...
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### Credible interval for a quantile from log-normally distributed data

Both reviewers of my latest article suggested better to work with credible intervals instead confidence intervals. Unfortunately, I am not familiar with Bayesian statistics. Until today, I was (...
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### Best way to show one Bayesian model is more certain and accurate than another, based on simulated data?

I'm trying to compare performance of two bayesian models $A$ and $B$ on simulated data. It's a recruitment curve fitting problem and I'm interested in how accurate these models are in estimating only ...
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### Estimating posterior of proportion of positives in population from per-observation probabilities

I have a sample from some population of 0s and 1s and need to estimate the posterior of the proportion of 1s in this population. But the catch is: for each observation in the sample I only have ...
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### Credible interval estimation for a difference of paired binomials

Assume one is given two series of binomially distributed data: $$X_{1k} \sim Binom(n_{1k}, p_{1k})$$ $$X_{2k} \sim Binom(n_{2k}, p_{2k})$$ $$k\in \{1\ldots K\}$$ The goal is to estimate $p_2 - p_1$ ...
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### Comparing three posterior distributions

I estimated a variable for three different species and have a posterior distribution of 4000 estimates for each species. Now I want to know if the distribution between species differs significantly. ...
196 views

### Differences between HPDI and PI intervals

In Bayesian statistics, we may want to determine at what interval for example 95% of the posterior probability exists. For this we may want to use the Highest Posterior Density Interval (HPDI) which ...
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### Converting a confidence interval into a credible interval

The problem of correctly interpreting confidence intervals has been discussed at length here. I have a related question which I believe may be a useful contribution: Frequentist probabilities by ...
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### Are HPD intervals invariant to reparameterization?

Suppose I have a parameter (or just any random variable) $\theta$, which we can assume to be absolutely continuous. If I compute a Highest Posterior Probability $I$ for $\theta$ and another one (let's ...
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### Bayesian Credible interval in Poisson Regression

Assume that $\pmb{y} = (y_1,...,y_n)$ are count data which depends on a dummy predictor $\pmb{x}$ (x = 0 if male, x = 1 if female) such that : \begin{align} \pmb{y} \sim Poisson(\lambda) \end{align} ...
1 vote
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### How to compute a 95% credible interval for a small sample size with little prior information?

Say I have the following empirically measured data describing a parameter of interest: x = c(12, 4, 6, 8, 5, 12, 12, 10, 6) where x is a continuous random variable....
510 views

### Finding changepoints in a GAM?

I'm using generalized additive modeling to investigate the relationship between two variables, X and Y. I want to find changepoints--i.e., X values at which the slope changes direction. I can get ...
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### Convergence of credible regions on simple Bayesian model

Consider a basic Bayesian model : $$\begin{array}{rcl} \theta &\sim &\pi(\theta)\\ X_1, \cdots, X_n&\overset{IID}{\sim} &\mathcal{N}(\theta, I_d)\\ \end{array}$$ where $d$ is the (...
1 vote
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### How to find the credible interval on the difference between the means of two proportions in R?

I have two proportions of the beta-binomial family. x1=41, n1=88, x2=41, n2=90 (x= no. of successes; n=no. of trials). The beta prior shape parameters for the two proportions are alpha1= 20, beta1=26, ...
1 vote
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### How to find credible interval for multiple bayesian distributions that disagree?

Feel free to suggest changes to my terminology here, I don't think this is proper Bayesian analysis. I'm a scientist trying to produce a credible interval for an unknown experimental value X. The ...
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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 ...
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### Interval Estimation for a Change in a Binomial Proportion

I'm not sure how to estimate the confidence interval (CI) for a change in a small sample size binomial proportion using the same sample set both times. I have two methods that I would like to compare (...
1 vote
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### In estimating a posterior mean, should one use the entire density or the HPDI?

Recognizing that HPDIs are analogous to confidence intervals in frequentist statistics, if one calculates an HPDI for a posterior distribution and then wants to report a posterior mean, does it make ...
337 views

### Confidence vs credible interval for binomial probability

I have two related questions regarding the calculation of confidence intervals for a binomial probability and how they relate to credible intervals. (This must have appeared a thousand times- ...
1 vote
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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 ...
1 vote
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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%...
1 vote
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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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### How do I generate a confidence region for a set of sample from a bivariate posterior?

I have a set of samples generated from a posterior function as shown below: I want to generate a bivariate High Posterior Density (HPD) credible region for the samples as in the below example (\$\...