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 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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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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When does a Bayesian 95 % credibility interval have 95% coverage?

Consider the generative model $$ \begin{align} \theta &\sim \pi(\cdot \mid \phi),\\ y \mid \theta &\sim f(\cdot \mid \theta). \end{align} $$ Compute the posterior distribution $p(\theta \mid y)...
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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} ...
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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....
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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, ...
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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 (...
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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 ...
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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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Finding credible interval for $\mu_1-\mu_2$ when $X_i\sim N(\mu_1,\sigma^2)$ and $Y_i\sim N(\mu_2,\sigma^2)$

Let $X_1,X_2,\ldots,X_m$ and $Y_1,Y_2,\ldots,Y_n$ be independent samples from $N(\mu_1,\sigma^2)$ and $ N(\mu_2,\sigma^2)$ populations respectively where $\sigma^2$ is known. I need to find a $100(1-\...
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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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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 ($\...
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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 ...
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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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Finding a credible region with a normal posterior

I have a posterior distribution that is normal and I want to find a credible region for which $\mu$ lies. However, I am having trouble integrating the following posterior: $\int \pi(\mu|x) = \int_{0....