# Questions tagged [posterior]

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

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### Finding the posterior mean

I have been trying to solve the following problem: Suppose $X_1,...,X_n$ are iid exponential random variables, with density $f(x;\theta) =\theta e^{-\theta x}$ ,and let us suppose that we have a prior ...
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### Finding which distribution the posterior is

I'm trying to teach myself Bayesian statistics and am currently trying find the posterior distribution on the following problem: Suppose $X_1,...,X_n$ are iid exponential random variables, with ...
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### Bimodal posterior of ATE predicted via Bayesias Additive Regression Trees

I am using BART to estimate the ATE on a large (10k obs x 224 p) dataset with a binomial outcome. In short, I first model the risk of the outcome $Y$ given the $(Z,X)$ covariates, then, for a chosen ...
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### Interpretation of concentration of posteriors in the limit of infinitely many independent versus dependent random variables

Disclaimer: the setup and specific example may not be a minimal example to illustrate the point, but I am not well-versed in these topics enough to construct a smaller example without accidentally ...
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### Finding posterior probability mass function of binomial parameter

Question: Suppose a lot containing 1000 items is received from a supplier containing parameter (unknown) defective items. The past experiences with this supplier suggest that 5% of items in a lot are ...
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### Squared Error Loss for Bayesian estimator of Normal distribution

I'm following Brad Efron and Trevor Hastie book "Computer Age Statistical Inference" (link). In chapter 7, they begin to debate the James-Stein estimator by calculating the Bayes rule, or ...
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### The Bayes' Theorem Components of the Probability Output of a Classifier

Let's give a simple setup. I have $500$ photos of dogs and $500$ photos of cats, all labeled. From these, I want to build a classifier of photos. For each photo, the classifier outputs a probability ...
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### Posterior mean of $\mu$ in Bayesian Hierarchical model (Poisson-Gamma)

Chapter 7 of Jim Albert's book considers the case of using a hierarchical model, to estimate heart-transplant mortality rates ($\lambda_i$) from 94 hospitals, each with it's own exposure (# of ...