# Tag Info

### What is the posterior probability for flipping a coin, assuming a beta distribution as conjugate prior

First of all, you already know the coin is fair hence the next throw will have a 50% chance of head and 50% of tail. If you know the coin is fair, the posterior distribution is p = 0.5. Now, what if ...
Accepted

### How to interpret the population parameters of a Bayesian Hierarchical model?

I think I have found an explanation for why $\psi(\mu, \tau) := \exp(\mu + \tau^2/2)$ can be useful to answer the question "What is the population-mean of the $\mu_j$'s?": Imagine you have ...
1 vote

### How to interpret the population parameters of a Bayesian Hierarchical model?

EDIT - I want to add that I no longer think my answer below is correct (i'm still unsure as to what I think the answer is) but am leaving my answer up as it already has comments. (posting an answer to ...
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### How to interpret the population parameters of a Bayesian Hierarchical model?

the posterior of $\tau$ is not necesarily a Log-Normal distribution anymore (that was just our prior), so why would the posterior population distribution of $\mu_j$ still be a Log-Normal distribution ?...
• 816
Accepted

If I understand you correctly, the only distributions depending on $\sigma^2_{\mathbf{b}}$ are the prior distributions of $\sigma^2_{\mathbf{b}}$ and $\tilde{\mathbf{b}} \mathrel{:=} \mathrm{vec}(\... • 5,350 1 vote Accepted ### prior and posterior predictive distributions, Bayes Theory As Demetri says, the answer is right there - maybe an example helps? Consider$f(y^{new}=1|\theta ,y)=P(y_{f}=1|\theta)\$, i.e., the probability that the next attempt will be a success, assuming random ...
• 31.8k
You have the answer in your first line. The posterior predictive is $$p(y^{new} \mid y^{old} ) = \int_\theta p(y^{new} \mid \theta) p(\theta \mid y^{old}) \, d\theta$$ The functions in the ...