All Questions
Tagged with credible-interval confidence-interval
74 questions
6
votes
3
answers
747
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confidence intervals for proportions containing a theoretically impossible value (zero)
This is really a hypothetical question not related to an actual issue I have, so this question is just out of curiosity. I'm aware of this other related question What should I do when a confidence ...
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1
vote
1
answer
29
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Extract credible/confidence interval of a threshold in a Bayesian posterior draws distribution [closed]
I have a Bayesian model created through bayer package in R on which I need to calculate confidence/credible intervals for a ...
- 229
6
votes
2
answers
489
views
Highest-density vs equal-tailed confidence interval
When a sampling distribution is symmetric (and I'm okay assuming unimodal too, if necessary), it's natural to center confidence intervals around the point estimate. But for a skewed distribution (e.g. ...
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6
votes
1
answer
283
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Gaussian Process: confidence interval vs prediction interval vs credible interval
Let a distribution over functions be described by a Gaussian Process (GP) prior, following the notation of Rasmussen and Williams:
$$
f(\mathbf{x})\sim\mathcal{GP}(m(\mathbf{x}), k(\mathbf{x},\mathbf{...
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1
vote
1
answer
36
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Can we report a credibility or confidence interval for a quantity measured only once, but whose distribution is obtained by Bayesian methods?
Suppose you use Bayesian methods to calculate the probability density function (pdf) of a quantity of interest $X$, given its measured value $x$ (measured only once) and some other assumptions/...
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12
votes
1
answer
485
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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 ...
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0
votes
0
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27
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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 ...
user318514
5
votes
0
answers
145
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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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0
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0
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1k
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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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1
vote
0
answers
43
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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 ...
user233429
4
votes
1
answer
95
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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 ...
- 1,233
1
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1
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182
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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 ...
3
votes
0
answers
714
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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 ...
- 103
6
votes
2
answers
778
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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 ...
- 93
3
votes
0
answers
699
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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 ...
1
vote
0
answers
57
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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 ...
- 131
21
votes
4
answers
2k
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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 ...
- 2,187
2
votes
5
answers
242
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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 (...
- 179
2
votes
0
answers
366
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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- ...
- 5,359
1
vote
1
answer
138
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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 ...
- 57
0
votes
0
answers
85
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%...
- 83
3
votes
0
answers
152
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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 ...
- 217
2
votes
1
answer
528
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
724
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
1
answer
397
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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 ...
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2
votes
1
answer
66
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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 ...
- 1,256
6
votes
4
answers
3k
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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....
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0
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1
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114
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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 ...
user226073
1
vote
0
answers
139
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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 ...
16
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3
answers
913
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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 ...
- 1,188
6
votes
1
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651
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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 ...
- 1,909
0
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1
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1k
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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 ...
4
votes
1
answer
1k
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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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12
votes
1
answer
1k
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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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2
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1
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526
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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{...
3
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1
answer
2k
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Highest Posterior Density (HPD) region of the marginals vs. of the joint distribution
In a Bayesian context, to analyse the posterior distribution, one can define the Highest Posterior Density (HPD) region or interval as
$$\{\theta; \pi(\theta \mid x) \geq k\} $$
in both unidimensional ...
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41
votes
6
answers
7k
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If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
I'm very new to Bayesian statistics, and this may be a silly question. Nevertheless:
Consider a credible interval with a prior that specifies a uniform distribution. For example, from 0 to 1, where 0 ...
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0
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37
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Is it valid to average the credible intervals from many simulations to obtain an average credible interval?
I am currently doing a Bayesian analysis where as output, I obtain a a point estimate. Each point estimate has an associated credible interval. Now, I am hoping to do the analysis 1000 times, then ...
- 4,260
1
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2
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229
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What does Bayesian Comparison of Groups and Posterior Interval say about my Hypothesis?
I am comparing the score of two groups: A and B. The score is normally distributed and a two sample t-test yields a p-value >0.05. Therefore I have to reject the Hypothesis that there is significant ...
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2
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1
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346
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Confidence/credibility intervals for a bernoulli trial
Say we have
$$
X \sim \text{Bernoulli}(p).
$$ I am interested in finding a 95% confidence and credibility interval.
For the credibility, I am assuming a uniform prior, giving me a posterior ...
- 770
4
votes
0
answers
374
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Confidence Interval vs Credible Interval for the Variance
I understand the conceptual difference between confidence and credible intervals. But I have difficulties applying these concepts to my application.
I would like to know the concrete difference ...
- 435
4
votes
1
answer
150
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Numerical estimation of binomial confidence interval
I have two measurements from two different distributions. I know both of these distributions are binomial and I measure $k_1$ successes from $n_1$ trials for distribution 1 and $k_2$ successes from $...
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2
votes
1
answer
601
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Proof that the HPD region is the smallest
In one dimension it can be shown that the highest posterior density (HPD) interval is the shortest; I found a proof in Subjective and Objective Bayesian Statistics (Section 8.4) by S. James Press ...
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1
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0
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Are credible intervals confidence regions? [duplicate]
I understand that I'm asking a very pedantic question, but as far as I'm aware a confidence region is a multi-dimensional generalization of a confidence interval and therefore as a credible interval ...
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5
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1
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343
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Is there a Bayesian analogue to a simultaneous confidence band?
A simultaneous confidence band denotes the probability
$$p \big(\hat{f}(x) - w(\hat{f}(x)) \le f(x) \le \hat{f}(x) + w(\hat{f}(x)) \ \ \forall x \big)=1-\alpha$$
where $f$ a function of $x$, $\hat{...
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1
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1
answer
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Terminology in interval estimation
(1) Confidence intervals
(2) Posterior probability intervals
(3) Fiducial intervals
Is there some conventional term that encompasses these three sorts of intervals, but does not include prediction ...
- 11.1k
9
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1
answer
935
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Why is the Bayesian credible interval in this polynomial regression biased whereas the confidence interval is correct?
Consider the plot below in which I simulated data as follows. We look at a binary outcome $y_{obs}$ for which the true probability to be 1 is indicated by the black line. The functional relationship ...
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2
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0
answers
956
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Do I evaluate coverage of my credible interval correctly and what are reasons for off-nominal coverage?
For a simulation study I derived the posterior distribution of a parameter $\theta$ with data $D$ as $p(\theta|D)$. I can sample from the posterior, but there is no analytic expression. The posterior ...
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4
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1
answer
428
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Why is the $1-\alpha$ Bayesian credible interval for $\lambda \sim \chi^2_{v}$ have endpoints $\chi^2_{v, 1-\alpha/2}$ and $\chi^2_{v,\alpha/2}$?
Suppose that a posterior distribution $\lambda$ has distribution $\lambda \sim \chi^2_{v}$.
Then, it is often written that a $1-\alpha$ Bayesian credible interval for $\lambda \sim \chi^2_{v}$ will ...
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4
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1
answer
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Is It Ever Appropriate to Treat a Bayesian Credible Interval as a Frequentist Confidence Interval?
I know that a bayesian credible interval and a frequentist confidence interval measure very different things, and have different interpretations. However, is it ever appropriate to treat a bayesian ...
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