All Questions
Tagged with prior self-study
55
questions
2
votes
1
answer
71
views
Using old posterior as new prior given new data [duplicate]
Suppose I have some data, and use this data to create a posterior distribution.
Now suppose I have some new data that I believe is from the same population as the data before. Can I now use my old ...
- 163
1
vote
0
answers
441
views
Reference prior of normal distribution with unknow mean and variance
Problem:
Assume that $X|\theta \sim N(\theta, \sigma^2)$ for unknow $\theta$, and unknown $\sigma$.
a. Find the reference priors of $(\theta, \sigma)$, when $\sigma$ is of interest.
b. Find the ...
- 327
0
votes
0
answers
538
views
To calculate Bayes estimator for $\theta $ using squared error loss function
The life of an electric bulb, X (in hours), follows the exponential distribution with mean life $ 1/ \theta $ , where $ \theta(>0) $ is an unknown parameter. The prior distribution of $ \theta $ ...
- 377
8
votes
1
answer
767
views
Decision Theory: Why is it called a "least favorable prior"?
I'm currently reading the chapter on Statistical Decision Theory in Larry Wasserman's "All of Statistics". Reading the section 13.4 about Minimax Rules he introduces the so called Least ...
- 223
-1
votes
1
answer
74
views
How are these priors generated? [closed]
I am trying going through an exercise, I don't understand how the information provided in the text below transitions into the parameters displayed in the beta priors. How are these informative priors ...
4
votes
1
answer
451
views
Showing $X\sim \operatorname{Poi}(\lambda)$ is minimax
Assume that $X$ has $\operatorname{Poisson} (\lambda)$ distribution and the loss function is $\ell(\lambda,a)=\frac{(\lambda-a)^2}{\lambda}$. Now, I want to show that $X$ is minimax. A hint that is ...
- 703
0
votes
1
answer
102
views
Showing that a posterior is Normal given improper prior
I am having difficulty showing the following problem and I suspect it has something to do with my lack of understanding of the question. The question is this:
Suppose we have an improper prior ...
- 125
2
votes
0
answers
42
views
Why do we reparameterize before assigning a hyperprior distribution?
I am studying hierarchical models, and trying to understand a point in the book where they try to decide on a non-informative hyperprior distribution.
The hyperparameters is $\alpha$ and $\beta$ for a ...
- 83
1
vote
1
answer
607
views
Find the prior distribution for the natural parameter of an exponential family
Show that for the binomial likelihood $y$ ~$Bin(n, \theta)$, $p(\theta) \propto \theta^{-1} (1-\theta)^{-1}$ is the uniform prior distribution for the natural parameter of the exponential family.
I am ...
- 83
0
votes
1
answer
395
views
posterior distribution of a Poisson mixture model
This is a Poisson-gamma model with mixture prior, thus mixture posterior. I am having some trouble finding the posterior weightings.
I have the prior weightings $p_1=1/3$; $p_2=2/3$. The 2 component ...
- 330
0
votes
0
answers
47
views
Using a beta-binomial model to estimate the average for a uniform prior [duplicate]
Say we had a sample of 100 people who were asked how many days during the last week they drove their car. Let's say the resulting frequency table is as follows:
Days, frequency
0, 1
1, 5
2, 3
3, 15
4, ...
- 13
0
votes
1
answer
179
views
How to calculate the expected value of k heads in this case?
I'm having some trouble on how to tackle the following problem
$X_1$ is a random variable with probability density $f(x)$ in the range $[0,1]$. A value of $X_1$ is picked, call its value $p$. A coin ...
3
votes
0
answers
317
views
How do I choose a prior for this hierarchical model? (Kruschke book)
I am working through Kruschke's "Doing Bayesian Data Analysis",
currently working on the Hierarchical models chapter. The book uses
JAGS for MCMC.
One of the exercises asks the reader to compare two ...
- 31
1
vote
1
answer
708
views
Bayesian Homework: Uniform Prior
Suppose posterior density of parameter $\theta$ is
$$\pi(\theta|\mathbf x)=\frac{\Gamma(5)}{\Gamma(3)\Gamma(2)}\theta^{3-1}(1-\theta)^{2-1}.$$
Now I have to find which of the two hypotheses $H_1:\...
- 357
2
votes
0
answers
748
views
Posterior distribution of Bernoulli distribution
The pdf of X | $\theta$ is given by $\theta^x (1- \theta)^{1-x}$
and its prior distribution is given by $p(\theta) \frac {1} {B(\alpha, \beta)} \theta^{\alpha - 1} (1 - \theta)^{\beta - 1}$
where $...
