# Questions tagged [posterior]

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

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### Does a conjugate prior always exists? [duplicate]

Are there distributions where no conjugate prior exists? Is there a necessary and/or sufficient condition which guarantees the existence of a conjugate prior? Edit: Why has this question been closed? ...
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### Can the posterior mean always be expressed as a weighted sum of the maximum likelihood estimate and the prior mean?

See this question. Is this always true? Can the posterior mean always be expressed as a weighted sum of the maximum likelihood estimate and the prior mean (after choosing some appropriate prior)?
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### poisson posterior = gamma function x uniform prior?

I was reading the section 3.2 of this paper. Above equation (3.2), the authors say "The posterior on the background estimate is then conservatively taken to be the Poisson posterior using a ...
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### Under what circumstances can an improper prior be used in bayesian analysis?

I am attempting to gain some intuition about the use of priors in bayesian analysis. I have read in some instances that an improper prior can be used when no information is known. However here is my ...
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### Question on working out a pdf from a posterior distribution

Need help with part (a) of this exercise. The exact step I'm concerned about is calculating the pdf from the relationship given in the exercise. I will appreciate any explanations on how should I ...
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### Uncertainty and distribution of a percentile

In a Bayesian analysis (Normal case), it is possible to obtain a posterior distribution of the mean and variance. We can also obtain quantiles, median,... of these distributions. My question now is: ...
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### What is the correct procedure for posterior inference about the cumulative distribution $F(y|\theta)$?

Let $y$ follow $f(y|\theta,x)$ with $\theta$ parameters with prior $\pi(\theta)$ and $x$ covariates with distribution $p(x)$. Let $p(\theta| D)$ be the posterior distribution of the parameters, where ...
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### Posterior density for normal distribution

I have that $Y_i$ has distribution $N(\beta x_i^2, 1)$, $i=1 \dotsc n$ where $\beta$ has a prior distribution $N(0, \sigma^2)$. I need to calculate the posterior density of $\beta$, find its mean and ...
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### Is there a way to measure the degree of correlation between two posterior distributions?

I have the following two distributions of MCMC samples from a Bayesian analysis and want to know the extent to which values from the first distribution are correlated with those from the second. Is ...
Usually, in an experimental scientific paper where we have observations $X$ taken in laboratory conditions, we either reject some model $\mathcal{M}$ under the basis that $P(X \mid \mathcal{M}) \ll 1$,...