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.
170
questions
2
votes
1
answer
99
views
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 ...
- 41
0
votes
0
answers
8
views
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 ...
- 13
0
votes
0
answers
50
views
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 (...
- 35
0
votes
0
answers
26
views
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 ...
- 211
3
votes
1
answer
35
views
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 ...
- 131
0
votes
1
answer
26
views
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 $p_2 - p_1$ ...
- 903
2
votes
1
answer
106
views
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. ...
- 271
3
votes
1
answer
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 ...
- 359
2
votes
0
answers
19
views
How to compute a rectangular credible region from samples
Given high-dimensional Monte Carlo samples $\bf{X_1},...,\bf{X_N}$ from a probability distribution $p({\bf x})$ in $\mathbb{R^d}$, I want to estimate a rectangular highest-density credible region for $...
- 31
7
votes
1
answer
173
views
Why do Bayesians care about the frequentist properties of Bayesian credible intervals?
I've been doing some reading on the topic of credible vs confidence intervals but unfortunately it feels like the more I read the more I'm confused. There seems to be a general sense or consensus that ...
- 151
0
votes
0
answers
26
views
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 ...
user318514
1
vote
0
answers
42
views
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 ...
- 151
2
votes
1
answer
286
views
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 ...
- 621
0
votes
0
answers
76
views
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.
...
- 43
0
votes
0
answers
109
views
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'...
- 16
0
votes
0
answers
107
views
Limit of $\frac{\lambda}{\chi _{2Y}^{2}}$ as $Y \sim \textrm{Poisson}(n\lambda)$ and $\lambda\to\infty.$
There are the following lines in Casella & Berger on page 438, before the equation (9.2.22):
..., write $$\lambda = \frac{\lambda}{\chi _{2Y}^{2}}\chi _{2Y}^{2}$$
where $\chi _{2Y}^{2}$ is a chi ...
- 29
3
votes
2
answers
132
views
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 ...
- 2,160
1
vote
0
answers
49
views
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 ...
- 61
5
votes
0
answers
131
views
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 ...
- 73
0
votes
0
answers
1k
views
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 ...
- 1
1
vote
0
answers
41
views
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 ...
user233429
4
votes
1
answer
92
views
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 ...
- 1,223
1
vote
1
answer
168
views
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 ...
3
votes
0
answers
505
views
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 ...
- 103
0
votes
1
answer
51
views
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 ...
1
vote
0
answers
234
views
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, ...
6
votes
2
answers
877
views
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)...
6
votes
2
answers
635
views
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 ...
- 93
4
votes
1
answer
188
views
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 ...
- 2,663
2
votes
1
answer
131
views
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}
...
- 430
1
vote
0
answers
87
views
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....
- 21
3
votes
0
answers
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 ...
3
votes
0
answers
41
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 (...
- 2,436
1
vote
0
answers
50
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, ...
- 21
1
vote
0
answers
50
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 ...
- 131
19
votes
4
answers
2k
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 ...
- 2,019
2
votes
5
answers
235
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 (...
- 179
1
vote
1
answer
104
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 ...
- 587
2
votes
0
answers
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- ...
- 4,110
1
vote
1
answer
116
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 ...
- 57
3
votes
1
answer
62
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 ...
- 107
1
vote
0
answers
22
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 ...
- 58.1k
0
votes
0
answers
83
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%...
- 73
1
vote
2
answers
39
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 ...
- 61
0
votes
1
answer
185
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} = \...
3
votes
0
answers
134
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 ...
- 217
2
votes
0
answers
410
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 ...
- 2,077
2
votes
1
answer
422
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 ($\...
- 31
7
votes
0
answers
584
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 ...
1
vote
0
answers
332
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 ...
- 1,207