All Questions
Tagged with prior mathematical-statistics
23
questions
1
vote
0
answers
32
views
How to interpret a noninformative joint prior?
I am currently working on a homework assignment and have the following question:
$\theta_1$ and $\theta_2$ are parameters of interest and $y_1$ and $y_2$ are the likelihood functions which are $\text{...
- 11
8
votes
2
answers
209
views
Do we ever use the prior predictive distributions of Bayesian Statistics?
As my question states, I am wondering if there is any chance we use the prior predictive distribution. I am studying Bayesian Statistics and have understood what it is. It is a must to go through in ...
- 81
4
votes
1
answer
243
views
Using Jeffreys prior for Bernoulli distribution to find the prior of a transformation on p
The question goes like this: Use Jeffreys prior for Bernoulli distribution and find the prior for $\eta$ where: $$\eta(p) = \left(\frac{p}{1-p}\right) $$
So $\eta$ here is some kind of a ...
- 543
0
votes
0
answers
136
views
How do I combine two beta priors?
The problem is,
Manufacturer receives 30% chips from A, and 70% chips from B.
Both A and B has Beta prior distribution for defective rate.
During inspection of 100 chips, 10 chips were found to be ...
- 1
1
vote
0
answers
172
views
In Bayesian hierarchical models, what is the difference between an Empirical Bayesian approach to parametrising priors vs using flat hyperpriors
Say I have a simple hierarchical model, where:
$y_{g,i} = \beta_g x_{g,i} + e_{g,i}$
where $g$ represents the group, $i$ represents the individual within the group, and $e$ is the error. So the ...
- 71
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
1
vote
0
answers
83
views
How to get prior distribution based on confidence interval [closed]
If we have mean value and 95% confidence interval of a parameter. For example, sensitivity = 0.5, CI = [0.2,0.78](as you can see, it is asymmetric)
How to decide the prior distribution?
How to ...
- 11
2
votes
0
answers
186
views
When does this prior dominate likelihood?
This is a simple Bayesian inference problem, where we are trying to infer some weight parameter $w$. Our posterior distribution is
$$ P\propto \exp\left(-\frac{1}{\sigma^2} w^Tw\right) \exp\left(-f(w)\...
- 281
1
vote
0
answers
147
views
Prior for Variance Covariance Matrix [closed]
Why in Bayesian Hierarchical Modelling the prior corresponding to a Variance Covariance Matrix is taken to be Inverse Wishart Distribution not Wishart Distribution?
- 41
2
votes
1
answer
455
views
Regarding the use of non informative priors
I am a beginner to Bayesian analysis and I am trying to fit a logistic regression model using Bayesian approach. For the prior distribution of the $\beta$ regression coefficients , I used a non ...
- 889
-1
votes
1
answer
37
views
Bayesian estimation Prior adaptation [closed]
I have a dataset of 1 dimensional 20points as prior information, so assuming prior distribution to be Gaussian distribution we can easily find its variance and mean. Now we will use this prior finding ...
- 21
1
vote
1
answer
124
views
Bayesian Inference & Determining the Prior
I have a dataset made up of the date (YYYYMMDD) of a specific event, with the time period spanning from 1970-2015.
I want to compare two time periods of 10 years each, and look at the yearly total ...
- 13
1
vote
0
answers
25
views
Linear regression - Bayesian Predictive distribution
I am trying to answer a question about linear regression but i am stuck:
$y=w \cdot x + \epsilon, \epsilon \sim N(0,\alpha)$
i am also given a prior:
$w\sim N(0,\beta)$
from which i was able to ...
- 11
0
votes
1
answer
494
views
Generating data from the posterior distribution
Let
$$p(D \mid \mu,\sigma^2) \sim \mathcal{N}(\mu,\sigma^2)$$
where $D=(x_1\ldots x_n)$ is my data.
I imposed a normal prior on the mean as
$$\pi(\mu) \sim \mathcal{N}(\mu_0,\sigma_0^2)$$
Using Bayes, ...
0
votes
1
answer
130
views
How to justify using Beta distribution as a prior distribution in the following problem
Let $\theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes ...
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