# Questions tagged [conjugate-prior]

A prior distribution in Bayesian statistics that is such that, when combined with the likelihood, the resulting posterior is from the same family of distributions.

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### Variance of multinomial and Dirichlet-multinomial distributions

I have an application where I would like to sample from a multinomial distribution, but I am concerned that the variance will be too low. As an alternative, I am considering the Dirichlet-multinomial ...
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### How do I determine my Bayesian sampling size when comparing two proportions?

I am currently working on writing a simulation in R to compare the results of Frequentist vs Bayesian when it comes to two-proportion hypothesis testing. For the Bayesian side, I am simply using a ...
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### Updating conjugate priors with noisy observations

I'm considering a problem that has been partially addressed elsewhere: Bayesian updating with conjugate priors using the closed form expressions but now I have an added twist. My samples are drawn ...
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### why use MH for Gaussian prior when its the conjugate prior

As I understand, gaussian likelihood function has a conjugate prior for μ which is also a gaussian. In that case, the posterior can be derived in closed form. Why do some many papers use metropolis ...
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### Bayes Factor and likelihood for two sample from different distributions?

I'd like to calculate Bayes Factor for two-sample t-test $H_0: \mu_1=\mu_2$ (model $M_0$) against $H_1: \mu_1\not=\mu_2$ (model $M_1$) My data are: $x_1,x_2,\ldots, x_{n_1}\sim N(\mu_1, \sigma)$ ...
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### Calculating the parameters of a Normal distribution using alpha and beta from Inverse-gamma (conjugate prior)

How is it possible to calculate the variance $\sigma^2$ for the Normal distribution if only $\alpha$ and $\beta$ (based on data) from the Inverse-gamma distribution are available? I followed the ...
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### Conjugate beta / interpretation of the "continuous binomial" signal

Note: this question has significantly evolved, thanks to inspiring comments by Tim. Assume there is some "truth" $x\in[0,1]=Beta(1,1)$ that is signaled with some precision. I assume that the ...
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### Posterior probability when data consists of $k$ largest of $N$ samples

Given an underlying unknown distribution, I sample $N$ numbers. From those $N$ numbers I take the highest $k$ numbers. How do I model the posterior probability from those $k$ numbers. I know I can ...
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### Prior elicitation with Inverse Gamma and parametrization issue

This is a homework problem. I am very new to Bayesian conjugate analysis, so hang on with me. I have a sample $(x_1...x_n)$ of $n=20$ observations from an experiment. These observations are breakdown ...
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### How to determine whether a given likelihood function has a conjugate prior? [duplicate]

Does there exists a certain formal procedure one has to go through before being able to claim that no conjugate prior $p(\theta)$ exists for the given likelihood function $p(X | \theta)$? In other ...
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### Bayesian analysis and Lindley's paradox?

I have this problem I am trying to wrap my head around that my friend's professor created. Can anyone give me some hints on how to get started, particularly in parts b and c? I have an understanding ...
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### Can anyone explain conjugate priors in simplest possible terms?

I have been trying to understand the idea of conjugate priors in Bayesian statistics for a while but I simply don't get it. Can anyone explain the idea in the simplest possible terms, perhaps using ...
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### From a Bayesian practitioner's standpoint, what are the specific conditions to decide on whether we have conjugacy or not?

I've been learning Bayesian statistical analysis on my spare time using textbooks, videos on YT, etc. I'm slowly going up that mountain. Please correct me if my wording below is poor or ask for ...
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