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.

Filter by
Sorted by
Tagged with
2
votes
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 ...
1
vote
0answers
25 views

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
0answers
19 views

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
0answers
19 views

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 ...
16
votes
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 ...
0
votes
0answers
6 views

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 ...
2
votes
5answers
192 views

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 (...
0
votes
0answers
7 views

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 ...
0
votes
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 ...
0
votes
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- ...
2
votes
0answers
75 views

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-\...
1
vote
1answer
32 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 ...
3
votes
1answer
24 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 ...
1
vote
0answers
16 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 ...
0
votes
0answers
30 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%...
1
vote
2answers
27 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 ...
0
votes
0answers
14 views

What is the distribution of the actual parameter given an estimate with credible interval or confidence interval?

Let's assume we have a variable $X$. Some authors said that X is distributed normally with mean $X_m$ with credible interval $(X_{m1},X_{m2})$ and SD $X_s$ with credible interval $(X_{s1},X_{s2})$. We ...
0
votes
1answer
53 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} = \...
0
votes
0answers
51 views

Estimate with known sample mean, sample size, prior mean, prior standard deviation?

I want to estimate the actual "eval" of a chess move (in this case, expected win rate - expected loss rate, ranging from -100 to +100). I have empirically calculated that on average, random ...
1
vote
0answers
20 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 ...
0
votes
0answers
42 views

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 ...
2
votes
0answers
16 views

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 ($\...
4
votes
0answers
70 views

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 ...
0
votes
0answers
8 views

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 ...
1
vote
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 ...
1
vote
0answers
74 views

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 (...
2
votes
0answers
68 views

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 ...
0
votes
0answers
27 views

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....
1
vote
1answer
70 views

How to best characterize uncertainty for an incidence rate? [duplicate]

Here is the scenario I am trying to model. I have a population of people who are susceptible to developing a disease. I observe each person for a different amount of time, summing to a total of 3000 ...
1
vote
1answer
42 views

Is confidence interval determined before observing data?

My professor is comparing the frequentist confidence interval and the bayesian credible interval. He claims that a confidence interval is determined prior to observing the data, while the credible ...
6
votes
4answers
457 views

Interpretations of negative confidence interval

Let's say I measured the weights of 50 chickens from my family farm, which keeps 1000 chickens. The sample mean is 5 kg, SEM is ± 3 kg, and the 95% confidence interval is 5 ± 3 * 1.96 = -0.88 kg to 10....
2
votes
1answer
64 views

One- vs two-sided credible interval for Poisson process with all zero counts

In a related question, I asked about a confidence interval for the estimate of the mean of 50 observations of a Poisson random variable, for which all 50 observations had a count of zero. In the ...
9
votes
1answer
1k views

Posterior variance vs variance of the posterior mean

This question is about the frequentist properties of Bayesian methods. Suppose we have data ${\bf y}$ generated from a distribution with a single parameter $\theta$, equipped with a prior $\pi(\...
7
votes
3answers
678 views

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 ...
0
votes
1answer
64 views

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 ...
1
vote
0answers
58 views

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 ...
15
votes
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 ...
0
votes
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 ...
0
votes
1answer
39 views

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 ...
6
votes
1answer
294 views

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 ...
1
vote
2answers
41 views

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 ...
1
vote
0answers
38 views

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 ...
1
vote
0answers
25 views

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 ...
0
votes
1answer
433 views

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 ...
4
votes
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 ...
0
votes
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 ...
2
votes
1answer
111 views

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. ...
10
votes
1answer
450 views

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 ...
2
votes
1answer
89 views

What formula for a Confidence Interval of the difference in proportions when sample sizes are small

Suppose that we are interested in comparing two approximately normal sampling distributions described by random variables $ \displaystyle \frac{Y_1}{n_1} = N(p_1,p_1q_1) $ and $ \displaystyle \frac{...
0
votes
0answers
30 views

Highest posterior interval and monotone changes of variables

Suppose $X$ is distributed with a unimodal pdf $f(x)$ and let $Y = g(X)$ for some strictly monotone function $g$. Hence $g$ is invertible. Is there an analytically tractable relationship between the ...