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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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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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 ...
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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 ...
213 views

Predict credible interval of Poisson-distributed response based on Lambda credible interval

I am approaching Bayesian inference. Could you review my steps and give me a hand with my model predictions? I am using a N-mixture model to predict how many individuals N of a rare species inhabit a ...
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credible intervals for functions of hyperparameters

If I have a statistic $\nu(x, y)$ which is a function of hyperparameters (say just two for ease of explanation) $x$ and $y$ of a distribution $F(t|x , y)$ and associated prior $g(x,y)$ which is the ...
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Constructing credible interval for store opening times

Overview: Suppose I have a log which records the time at which customers visit a store. For the sake of this example, say I have 10 stores in the dataset. Example data for Store 1: Customer 828: 9:...
159 views

Joint credible regions from MCMC draws

Lets say I have $n$ posterior samples of $\theta_1$ and $\theta_2$. I suppose that any region $R$ which contains exactly $(1-\alpha)n$ of the points will be an approximate $(1-\alpha)\times100$ ...
533 views

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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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 ...
276 views

Computing Highest Density Region given multivariate normal distribution with dimension $d$ > 3

Background: Suppose I have a unimodal symmetric distribution of dimension $d$ > 3 such as the multivariate normal distribution ~ N(0, H), where H is a known $d$-dimensional covariance matrix. ...
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Bayesian credible interval calculation: posterior distribution or marginal distribution

Let's say we want to obtain the 95% credible interval for theta, where theta|x ~ Beta(a,b), which one of the following is correct and why? [E(theta|x) - 2*se(theta|x), E(theta|x) + 2*se(theta|x)] [E(...
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How to calculate a 95% Credible Interval for a Bernouli sampling in R?

How does one calculate a 95% Credible Interval for Bernouli sampling? I have looked into the package emdbook and the function tcredint() but i am unsure if this the way to go. If anyone has ...
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Estimate the mean and variance 95% HPD credible region using Bayesian inference

I have the following data: 31.0, 30.5, 20.6, 27.2, 26.5, 28.1, 25.8, 29.6, 30.0, 25.8, 25.1, 27.9, 23.0, 29.4, 28.7, 25.0, 31.1, 24.8, 24.8, 27.0, 22.3, 29.5, 31.5, 26.2, 24.6, 23.2, 25.7, 24.2, 28.8,...
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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 ...
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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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Finding credible intervals for hyperparameters in Bayesian inference

I'm trying to use Bayesian inference to fit and interpret a linear model of the following form: $$y=X\beta + \epsilon \hspace{1cm} \text{where } \epsilon_i \sim \mathcal{N}(0,\sigma^2)$$ The ...
370 views

Reduce credible intervals in Causal Impact model

I'm hitting an issue with a causal impact model that I'm building. I'm trying to create a counter factual for daily sales at one store (nseasons = 7). I've included sales for 5 other stores nearby. ...
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Credible Interval Format?

I'm reading a datasheet that has listed a "credible interval". By my novice understanding, it is similar to a confidence interval. It is formatted like this: (-8.13, -2.69). So would the -8.13 be the ...
131 views

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 ...
260 views

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 ...
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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 ...
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 ...