Questions tagged [prior]
In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.
1,008
questions
9
votes
2
answers
426
views
How is data generated when using an improper prior
Let $X$ be an $\mathcal{X}$ valued random variable. We are doing Bayesian statistics. Suppose that $\theta$ is a $\Theta$ valued random variable with known prior distribution $\Pi$ and that the ...
- 456
1
vote
0
answers
22
views
Can we solve by hand the early exit multi-class classification problem? [closed]
Problem: Find a solution $\hat{\varepsilon}$ of the following minimization problem
\begin{align*}
&\min_{\varepsilon \in \mathbb{R}^M} \sum_{h=1}^M \varepsilon^h \hat{R}^h+\beta \sum_{h=1}^M \...
- 111
0
votes
0
answers
23
views
Random sequence generator algorithm non informative piror distribution
I want to conduct a Bayesian statistical analysis of a sequence generation phenomenon.
The sequences generated contain elements from a known alphabet.
Working on that, I have tried to define the prior ...
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
1
vote
0
answers
35
views
How to derive conditional destribution of MVN variable
I am working with following model specifications (Regression_ Modelle, Methoden und Anwendungen-Springer-Verlag Berlin Heidelberg (2009), p. 147):
$$Y \sim MVN(X\beta, \sigma^2I)$$
$$\beta|\sigma^2 \...
- 137
1
vote
1
answer
66
views
Full conditional posteriors
so up to now I dealt with posteriors in the form of:
$$p(\theta|x) \propto p(x|\theta) p(\theta)$$
No we started to model a linear regression with the bayesian approach:
$$Y \sim MVN(X\beta, \sigma^2I)...
- 137
0
votes
0
answers
24
views
How to sample from the prior predictive distribution with the BSTS R package?
Assuming I have to use the bsts package in R, I'm trying to understand the degree to which my prior distribution choices (implicit or otherwise) are consistent with ...
2
votes
0
answers
57
views
Credible intervals with parameter near boundary
When doing Bayesian inference on a parameter that is bounded, often we use priors that approach 0 as the parameter approaches the boundary. For example, when estimating $(\mu, \sigma^2)$ for normal ...
- 3,750
0
votes
0
answers
21
views
How to select a proper prior to control the time dependent structure of variable?
I am new in analyzing RCT data and not familiar with the techniques that are always used in RCT analysis.
I am analyzing a dataset of a study: An RCT study with 50 participants; the data was collected ...
- 250
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
1
vote
0
answers
27
views
Understanding the Binomial likelihood notation
Let $X \sim Bin(n,\pi)$.
I don't understand why the binomial likelihood is then given by $f(x|\theta)=\binom{n}{x} \theta^x (1-\theta)^{n-x}$. Shouldn't it be $B(x|\pi,n)=P(X=k)=\binom{n}{k} \pi^k (1-\...
- 137
3
votes
1
answer
173
views
Bayesian linear regression: How to enforce constraint on the sum of coefficients?
I have a linear regression problem in which my $X$ matrix is not full rank. Here is a small example:
$$X =
\left[\begin{array}{rrrr}
-1 & 0 & 0 & 1 \\
1 & 0 & -1 & 0 \\
0 &...
- 431
6
votes
1
answer
156
views
Trouble understanding priors
The following comes from a book called Bayesian Statistics by Ben Lambert:
Assuming the following model for $r$ disease-positive people out of $n$ people:
$$Pr(Z=r, \theta) = {n\choose r}\theta^r(1-\...
- 163
3
votes
1
answer
111
views
Choosing Bayesian Priors [duplicate]
I am fairly new to Bayesian Modeling, however I am experimenting with such framework in order to produce several estimates.
The part I am struggling the most with is the selection of prior ...
4
votes
3
answers
109
views
How subjective are prior beliefs?
I find the term 'prior-beliefs' to be a little bit vague, what is acceptable to class as a prior belief in Bayesian analysis? For example, I could not look at any data and decide to myself "I ...
- 163