All Questions
Tagged with prior conjugate-prior
46
questions
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Picking parameters for beta prior
I have some data that I believe come from a binomially distributed population. A beta prior seems like an appropriate choice, but I don't have any very strong prior beliefs. I could use a less ...
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0
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103
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posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision
What is the posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision. Thus, what is the distribution of x given:
\begin{equation}
x \sim \mathcal{N}(x; \...
- 331
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17
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To derive Posteriors from Conjugate Priors, do we just multiply the terms in the PDFs with the parameters of interest?
Consider the beta-binomial model (beta prior, binomial likelihood). So we have$$
\begin{align}
P(\theta)&\sim \text{Beta}(\theta|\hat a,\hat b)
\propto \theta^{\hat a-1}(1-\theta)^{\hat b-1}\\
P(Y|...
- 55
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How to calculate the posterior distribution with a normal likelihood function and a prior that involves sigma
In the problem, the data X follows a normal distribution, or $f(x|\mu,\sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp(-\frac{1}{2}(\frac{x-\mu}{\sigma})^2)$. Let's say I know the value of $\sigma^2$ and ...
- 303
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Eliciting a Gamma informative prior in a Gamma–Poisson Bayesian problem
I employ the Gamma–Poisson conjugate family for my statistical model.
I want to use an informative prior.
From theory, I know that the values of the Gamma-distributed random variable lie within the ...
- 37
1
vote
1
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199
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Does the beta negative binomial (BNB) distribution have a conjugate prior?
BNB distribution is constructed using negative binomial and beta distributions, which are both exponential family, so my guess would be yes, there shoudl exist a conjugate prior in theory. But what is ...
- 173
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63
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How should I deduce the conjugate prior and corresponding posterior for a geometric distribution
The given pmf is for a geometric distribution and is $f(x_i|\theta) = (1-\theta)^{x_i - 1}\theta; ~x_i = 1, 2 ,\cdots, $ and the 1-parameter exponential family I have obtained is; $$f(x|\theta) = \exp ...
user365863
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1
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73
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Posterior distribution when the domain of the likelihood depends on the parameter
I am trying to calculate a posterior density given distribution and a prior. And I am a bit confused about how I should act as the domain of the distribution depends on the parameter.
I am talking ...
2
votes
0
answers
220
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Conjugate Prior for Multivariate Normal Variances and Correlations
Is there a way to separately specify conjugate priors for the variance and correlations of a multivariate normal? The inverse Wishart is conjugate if you want to specify the covariance, but covariance ...
- 1,135
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141
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References for the conjugate prior to the beta distribution? [duplicate]
The Wikipedia article about "Conjugate Prior" has a table containing information about Likelihood Distributions with their Conjugate Priors.
In the "Continuous Likelihood" table, ...
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1
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206
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The PDF of the Data (Marginal Likelihood) Given the Prior of a Gamma Distribution with Prior on the $ \beta $ Paraneter
Given a model where $ x_i | \beta \sim \mathcal{Gamma} ( \alpha, \beta ) $ where $ \beta \sim \mathcal{Gamma} ( \alpha0, \beta0 ) $, is there a closed form formula for the PDF of $ x_i $?
Namely, what'...
- 145
3
votes
2
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238
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The PDF of the Data Given (Marginal Likelihood) the Likelihood and the Prior of a Normal Distribution with Prior on the Mean
Given a model where $ x_i | \mu \sim \mathcal{N} ( \mu, \sigma^2 ) $ where $ \mu \sim \mathcal{N} ( \mu_0, \sigma_0^2 ) $, is there a closed form formula for the PDF of $ x_i $? Namely, what's $ p (...
- 145
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70
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Conjugate Hyperpriors
I heard it was possible to have a Bayesian model with likelihood, prior and hyperprior that has a posterior of closed form, by choosing a conjugate prior and conjugate hyperprior. But I struggle to ...
- 31
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2
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394
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If the prior and likelihood not be conjugate, how to get conditional distribution to sample from using Gibbs sampling?
I know that when prior is conjugate with the posterior, by writing the loglikelihood and log prior and eliminate the non-independent terms for each parameter one can get the conditional distribution ...
- 135
2
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379
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What if the prior not be conjugate with posterior in Bayesian learning?
I know that when the prior is conjugate with posterior then one can get an analytical representation for the posterior distribution, but what if these two are not to be conjugate? For example, I would ...
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