# 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 ...
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### Do most scientific discoveries commit the conditional probability fallacy?

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 $P(X \mid \mathcal{M}) \ll 1$,...