New answers tagged posterior
5
votes
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 ...
3
votes
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 ...
- 780
4
votes
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
0
votes
Accepted
Posterior Distribution in a Bayesian Multivariate Normal Model
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
2
votes
prior and posterior predictive distributions, Bayes Theory
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 ...
- 33.5k
Top 50 recent answers are included