# 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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0answers
23 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 (...
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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, ...
0answers
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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 ...
4answers
1k views

### 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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### Constructing a credible interval from 5 separate trials

So I have simulated data for 5 separate trials, all of which are simulations of a basketball game outputting the number of expected 3 throws. Now I'd like to compute the credible interval, assuming ...
5answers
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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 (...
0answers
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### Confidence intervals for measurements at slice level

I have kind of a practical statistics problem in which I am not sure what is the best way to proceed. Below is a fake but similar to the problem I am trying to solve. I have a sample of ...
1answer
28 views

### 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 ...
0answers
24 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- ...
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### How to explain the difference between confidence and credible interval?

The key difference between Bayesian statistical inference and frequentist statistical methods concerns the nature of the unknown parameters that you are trying to estimate. In the frequentist ...
0answers
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### Calculating credible intervals of group means with sum contrasts?

I have fit a Bayesian mixed-effects logistic regression with sum contrasts +/- 0.5. All predictors are binary. But now I don't know how to calculate the credible intervals for the reference level of ...
0answers
123 views

### Using a hierarchical model (on pymc3) to compute credible intervals for dependent proportions

I have a dataset composed of 2 conditions, each condition consists of 3 samples, each sample subdivided into different categories. I would like to compute 95% credible intervals for the proportions of ...
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### Point estimate and 95% credible interval

The text of the problem as follows: The data follows a normal distribution with $\mu$ and $\sigma^2$ unknown. We wish to perform inference on the mean selling price $\mu$. And our sample data are (...
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### How to determine the size of highest density region in high dimensions

I want to calculate the "size" of the highest density region (HDR) that contains p% of the total probability for multivariate samples of a Bayesian posterior obtained via MCMC. In 1D this "size" is ...
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### Do Bayesian credible intervals treat the estimated parameter as a random variable?

I read the following paragraph on Wikipedia recently: Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat ...
1answer
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### Likelihood, posterior, prior interpretation and credibility/confidence_level with bayesian/frequentist approaches

This question was originally posted on physics exchange but one advised me to transfer it here. I try to understand the following article : testing general relativity from curvature and energy ...
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### Why is a frequentist confidence interval equivalent to a credible interval with flat priors?

It's a commonly quoted result that frequentist confidence intervals are equivalent to a bayesian credible interval assuming a flat prior. Ignoring for now questions about invariance under ...
3answers
489 views

### 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 ...
1answer
945 views

### How should I treat categorical variables in Bayesian modelling

I have got a dataframe that contains three categorical predictors and one numerical response. I would like to compare their differences using posterior uncertainty intervals of MCMC draws. The reason ...
1answer
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### meaning of posterior distribution and credible internal

In Bayesian method, we can get a posterior distribution of a parameter. Now I want to do some simulation to know if the posterior distribution is the same as the true distribution. For example, mean ...
1answer
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### Interpretation of confidence interval in Bayesian terms

Motivation: I was standing in front of a class to introduce into the concept of confidence interval using the example of differences in means (purely frequentist setting) and I was torturing the ...
2answers
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### credible interval in bayes are higher than the nominal level

When I fitted the nonlinear regression using the openbugs, and calculated the 95% credible interval of the coefficient through the high density interval, I found that the total number of the credible ...
0answers
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### Monte Carlo integration for Bayesian parameter estimation

I want to determine the credible interval of a quantity $\theta_1$. I want to make this estimate using observed data by assuming a certain model which depends on $\theta_1$ as well as about n=15 ...
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### Computing the credible region from a pre-computed list of function evaluations

I have a nonlinear function of four variables $f(x_1,x_2,x_3,x_4)$. This function outputs three things: $[y_1, y_2, y_3]$. (In reality, the function $f$ is a simulation which solves the equations of ...
1answer
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### How do I calculate the confidence interval from a Bayesian analysis

I got the posterior distribution of a parameter from Bayesian analysis. I want to express it as confidence interval. If I plot the empirical cumulative distribution function of the parameter and ...
1answer
613 views

### A question on Bayesian credible interval vs frequentist confidence interval

The difference of Bayesian credible interval (BCI) and the frequentist confidence interval (FCI) is well explained with a nice example in this answer. Here is my own summary of the situation in the ...
1answer
99 views

### Find bayesian credible Interval

I am taking this example from here. They have given the steps but i cannot understand them so a little dumbing down of answer is necessary or you can just explain the answer given there. its on page 5 ...
1answer
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### My credible interval never contains the true value when it is at the edge of the data

I am estimating an unknown variable which is between 0 and 1. I start off with a uniform prior on [0, 1]. Then I update it given some evidence (flip the coin a few times). Now I have a posterior. ...
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### The basic logic of constructing a confidence interval

Consider a model with a parameter of interest, $\theta$, and its point estimator, $\hat\theta$. For simplicity, assume $\hat\theta\sim N(\theta,\sigma^2/n)$ (in numerous instances this could be ...
1answer
89 views