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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Bayesian nonparametric estimate of median

I've been working on estimating the population median of a variable with a complex distribution that is not easily characterized as a parameterized probability distribution. So far, the best I have ...
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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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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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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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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 ...
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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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How to construct the highest posterior density (HPD) interval

Please, anybody could explain the steps to compute the highest posterior density (HPD) interval, when the posterior distribution is known? For instance, when the posterior distribution is Beta ...
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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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Is the pth percentile of a mixture distribution a weighted average of the pth percentiles of it's components?

Suppose Y is a mixture distribution defined as follows: If are beta distributed random variables (making Y a mixture of three beta distributions); and are the 95th percentiles of the densities of Y ...
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If I do the same experiment many times then does a 95% credible interval mean 95% of the time the true value lies within that range? [duplicate]

Its common misinterpretation of a 95% confidence interval to say that that 95% of the time the true value lies within that interval. However, in Bayesian statistics, the 95% credible interval ...
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Computing Bayesian Credible Intervals for Bayesian Regression

I understand the Bayesian regression approach, in which I compute the posterior distribution of the parameters $\theta_i$. Now I am interested in how to compute the credible intervals of the ...
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Credible intervals after Expectation Maximization

We are applying EM to a problem where we have N items to classify (binary classification, 0 or 1 ) for which a correct classification exists but is unknown, and a set J of "judges" that performs the ...
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Bayesian model selection and credible interval

I have a dataset with three variables, where all variables are quantitatives. Let call it $y$, $x_1$ and $x_2$. I'm fitting a regression model in a Bayesian perspective via MCMC with ...
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Likelihood Ratio Confidence Intervals and Credible Intervals for MCMC

I am fitting a 5 parameters model to some data using Maximum Likelihood and Non Informative Bayesian Inference using Metropolis-Hastings algorithm. From the maximum likelihood fit, i calculated the ...
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136 views

Parameters not in the credible interval interpretation in Bayesian model

I create a spline model in a Bayesian framework and all the parameters that are estimating the spline (the random effects of the spline) are lying between a Credible interval of negative something to ...
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Interpret credible intervals / HPD following posterior sampling

I am unsure on how to interpret credible interval results. How can credible intervals consist of negative numbers when the collected data only consists of positive numbers? I would expect that, given ...
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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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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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RMSE credible intervals for Gaussian Processes

I am trying to calculate a credible interval for the predictions I obtain from a GP regression problem. My objective is to compare the predictive performance of two models. I got out-of-sample ...
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How to find 95% credible interval?

I am trying to compute the 95% credible interval of the following posterior distribution. I could not find the function in R for it but is the approach below correct? ...
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Taking into account the uncertainty of p when estimating the mean of a binomial distribution

I have a binomial distribution with parameters $N$ and $p$, and the estimate for the mean of my distribution is N$\times p$. The values of $N$ and $p$ are such that we can use the Gaussian ...
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How to get multivariate credible interval estimate(s) / highest density regions (HDR) after MCMC

I'm estimating 15 parameters of my model using a Bayesian approach and a Markov Chain Monte Carlo (MCMC) method. My data after running a MCMC chain of 100000 samples is therefore a 100000×15 table of ...
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Confidence intervals fallacy once again — second attempt

You say (e.g here and here) The reason why it is won't to say there is a 95% chance the confidence interval contains the true parameter (or the probability of the interval containing the true ...
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Cross Validation and Sequential Monte Carlo (SMC)

Please bear with me, I am not a statistician. I have a likelihood $$\Pr (d|\vec{x},\vec{e})$$ where $d$ is a single datum, $\vec{x}$ are the model parameters, and $\vec{e}$ are known experiment ...
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Credibility interval for Model, M(A,B)

Supposing you've a model M(A,B) dependent on parameters A and B. You've successfully generated 10,000 samples from the posterior distributions for A and for B. The 2.5% and 97.5% quantiles of the ...
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Confidence Intervals vs. Credible Intervals for statistical inference in linear regression

Consider the following scenario featuring a linear regression analysis. In the left panel I have estimated the ordinary least square (OLS) regression line along with the 95% confidence intervals. In ...
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Applying Bayesian statistics to A/B testing, calculate credible intervals?

I do not know much about statistics but from my primitive research, I would like to explore how to apply Bayesian statistics in A/B testing. The best Bayesian-based A/B split test graphic calculator ...
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Should I have “Confidence” in Credibility Intervals?

Preliminaries First, I know that the Bayesian/Frequentist debate is rather long in tooth at this point, but I hope my question is sufficiently different from the others I reviewed on this site before ...
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The seemingly backward est. of confidence intervals in Winstein's example

My question is related to Winstein's explanation of the difference between confidence intervals and credible intervals. Please pardon my (at best) amateur rambling, but this has stumped me thoroughly ...
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How do I calculate the Credible interval of the effect size? (Bayesian framework)

I use R. I have a linear mixed model and I use its output to estimate my posterior distribution (with uninformative priors) using the function sim. I calculate the ...
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How to summarize credible intervals for a medical audience

With Stan and frontend packages rstanarm or brms I can easily analyze data the Bayesian way as I did before with mixed-models ...
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Different Confidence vs. Credible Interval (Continuous case, noninformative prior) [duplicate]

Okay, so, credible intervals aren't the same as confidence intervals. We all know that. In fact, they're only guaranteed to be the same when they're about a location or a scale parametre with a ...
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credible interval BCI in R

I used BCI to calculate the credible interval I had 3 paramters alpha,gamma and delta and the result is ...
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Mathematical proof that the posterior probability that a CI contains the true parameter is in $\{0,1\}$

There are great posts on confidence intervals, a subject that was brought up recently on this question, leading to an endogamous and circular surfing between CV classics, such as this one and this one ...
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What can we conclude from a Bayesian credible interval?

I learned that the credible interval does not have the frequentist property, but recently I read the following statements that derived from the credible interval/region: Point (0,0) is on the edge ...
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Credible set for beta distribution

How can I approximate beta distribution $\alpha=x+1$ and $\beta = 14-x$ to normal distribution? Or, could you please tell me how to calculate HPD credible set for beta distribution?
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Finding a scale matrix of multivariate Cauchy distribution given a border of credible region

I want to solve the following problem: I have a multivariate Cauchy distribution, centered at $\mu$, with unknown scale matrix $\gamma$. Now I receive a data point (blue $x$ in the picture) and my ...
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How to uniquely define the credible interval?

Consider we are in the Bayesian paradigm and consider that we know the posterior $P(\tau|d)$ of the single parameter $\tau$, whose max of the posterior is given by $\tau_{\text{best}}$. The credible ...
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Confidence and credible interval: cases

I am having difficulties in understanding these two approaches. Let's say given the data I compute both confidence and credible interval, then what is the intuition/interpretation of having: Big CI ...
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Bayesian analysis: Estimate whether a parameter is 0 or not

I have the following problem: I need to assess whether a given parameter $B$ is equal to 0. Let's consider the following model (my problem is more complicated but I think that this example is ...
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What is a Highest Density Region (HDR)?

In statistical inference, problem 9.6b, a "Highest Density Region (HDR)" is mentioned. However, I didn't find the definition of this term in the book. One similar term is the Highest Posterior ...
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Probability Interval for F(x) with Parameter Estimates from Bayesian Analyses

Problem: I estimated the shape $\alpha$ and scale $\lambda$ parameter of the Weibull distribution using Bayesian methods. That gave me a marginal posterior distributions for both parameters. ...
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credible interval equivalent of confint() for bayesglm() in Gelman et al's 'arm' package?

How do I extract a credible interval ala confint on a glm object when working with the object returned by bayesglm() in arm?
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Bayesian credible intervals: “superiority” even if 1 is included?

In a recent medical publication comparing a cardiac device to anticoagulation ("blood thinners") using a Bayesian statistical model to evaluate the efficacy of preventing strokes and cardiovascular ...
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Why would one use `random' confidence or credible intervals?

I was reading a paper recently that incorporated randomness in its confidence and credible intervals, and I was wondering if this is standard (and, if so, why it is a reasonable thing to do). To set ...
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Is there an article/book reviewing different methods for constructing posterior point/interval estimates?

Given a one-dimensional posterior distribution it is often the case that you want to calculate a point estimate and a credible interval for the corresponding parameter. There are, of course, many ways ...
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Hypergeometric: how do I construct a credibility interval around K (population successes) in R?

I have a problem for which I believe I should use the hypergeometric distribution, but I can't figure out how to do it in R. Say I have a bag of marbles with known number ($N$) of marbles, but the ...
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When do (and don't) confidence intervals and credible intervals coincide?

Yes, I know there are many questions on comparing these two types of intervals, but none of them appear to answer this exact question. Here is a blog post demonstrating one case where the two ...
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How do I correct for gender bias for Bayesian credible intervals?

Forgive me if this question is answered elsewhere - it may be all I need to be told is the correct terminology. I have a survey in which I ask a number of Yes/No questions (actually Yes/No/Don't know ...
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Pitfalls of posterior simulation when analysis didn't begin as Bayesian

I've got a situation where I'd like to evaluate a function of a fitted model, and account for the uncertainty in the fitted model. For example, say I want to calculate the minimum of the function $f(....