# 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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### Estimating a population proportion and credible interval from a biased stratified sample

I am attempting to calculate a point estimate and the upper 95th percentile (one sided credible interval) for a defect rate (i.e. a population proportion) using the results of a biased stratified ...
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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 ...
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### 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 ...
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### 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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### 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 ...
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### 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 ...
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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 ...
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### The Bayes credible interval / Bayes credible region of the posterior distribution of a multinomial Dirichlet conjugate pairs

I have a posterior distribution of Dirichlet form with new parameters (alpha1, x1), (alpha 2, x2) and (alpha 3, x3) and the posterior mode of each dependent variable as the Bayes estimator. I wish to ...
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### Credible intervals from bayesian NN misbehave

I am using Edward, to create a Bayesian neural network for non-linear regression. My training set consists of time series that all end at 0 but after doing inference the predictions (and thus the ...
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### What exactly does it mean that a 90% Credible Interval is computationally stable?

I was reading the rstanarm documentation and came across this about its use of 90% intervals as the default. I was hoping someone might be able to provide some clarification. Default 90% intervals ...