# Questions tagged [posterior]

Refers to the probability distribution of parameters conditioned on data in Bayesian statistics.

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### Find the posterior of Bernoulli likelihood and reparametrized prior

Supposed that we have $Y_{i}$ ~ $Bern(a)$, and an improper prior p of $Beta(0,0)$. Let $g(a)=\phi = \log(\frac{a}{1-a})$. We would like to find the posterior distribution of $\phi|y$. My trial: For ...
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### Posterior predictive distribution of Gibbs Sampling compared to original data

I have implemented a Gibbs sampler to simulate from the joint posterior: $ln(y_1),...,ln(y_n)|\mu,\sigma^2 ∼_{iid} N(\mu,\sigma^2)$ Where both $\mu$ and $\sigma^2$ was unknown. I have simulated values ...
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### Bound on the expectation of a function of random variable having a strictly log-concave probability density

let $\theta \in \mathbb{R}^d$ be a random variable having a strictly log-concave probability density function, i.e $$p(\theta) = e^{-\phi(\theta)}$$ where $\phi(\theta)$ is ...
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### 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. ...
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### Deriving Bayesian Credible Intervals for AUC using R brms

I am trying to estimate the posterior distribution for the AUC of a predictive biomarker using R brms. However, whenever I calculate the AUC using the posterior distribution of the model parameters, ...
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### Highest Posterior Density Interval (HPDI) using kernel

I'm trying to compute the 95% HPDI of a posterior from 10000 draws from a distribution. I've been instructed to use density() in ...
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1 vote
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### Posterior distribution of $\mathcal{N}(\theta, \theta^2)$ with normal prior

Are there any analytical/closed-form results on the posterior distribution of $x \sim \mathcal{N}(\theta, \theta^2)$ using a standard normal prior?
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1 vote