All Questions
Tagged with prior distributions
63
questions
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
3
votes
1
answer
115
views
Light tailed symmetric distribution
Is there a family of distributions that resemble the normal distribution (symmetric, spanning all real numbers, and approximately bell-shaped) but have lighter tails than normal distribution?
I'm ...
- 943
2
votes
2
answers
160
views
Find a likelihood to calculate a posterior probability
I am having trouble understanding a basic Bayesian inference exercise:
Suppose we are interested in inferring the proportion $\theta$ of
individuals in a given population suffering from a certain ...
- 121
5
votes
2
answers
265
views
Is a data size in a binomial distribution random variable?
Supposing that there is a binomial distribution ${\rm Bin}(m|N, \mu)$, I think usually $N$ and $\mu$ are parameters and not random variables (or events), thus the notation here ${\rm Bin}(m|N, \mu)$ ...
- 153
2
votes
1
answer
185
views
How to find the marginal prior distribution?
Suppose that $\beta$ has the following prior
$$
\beta|\zeta \sim f(\beta,\zeta)
$$
Then I know that the marginal prior distribution of $\beta$ is given by
$$
\int f(\beta,\zeta) d\zeta
$$
However, ...
- 273
2
votes
1
answer
283
views
Choice of prior to restrict coefficient to negative values?
I'm slightly embarassed to be asking this question, but I couldn't locate a satisfying reference. I'm a complete novice in Bayesian regression, working through the textbook Statistical Rethinking. In ...
- 540
1
vote
0
answers
81
views
The Elephant in The Room: How is Real-World Domain Knowledge Converted into Bayesian Priors?
I have been trying to look into the daunting problem within Bayesian Models: How is Real-World Domain Knowledge Converted into Bayesian Priors?
Logically speaking, it seems that Bayesian Priors can be ...
2
votes
1
answer
28
views
Drawing inferences from multiple modal estimates of a random variable
I'm working to elicit a probability distribution from the Survey of Private Dealers, a ~monthly survey concerning the future direction of certain financial random variables. Latest example here.
There ...
- 442
36
votes
2
answers
3k
views
How are Bayesian Priors Decided in Real Life?
I always had the following question: How are Bayesian Priors decided in real life?
I created the following scenario to pose my question: Suppose you are researcher and you are interested in studying ...
0
votes
1
answer
89
views
Conjugate Prior for Alpha Power Inverse Weibull Distribution
Let $X$ has Alpha Power Inverse Weibull (APIW) distribution with pdf
$f(x) = \frac{\log \alpha}{\alpha - 1} \lambda \beta x^{-(\beta+1)} e^{-\lambda x^{-\beta}} \alpha^{e^{-\lambda x^{-\beta}}}, \; x&...
- 41
0
votes
1
answer
130
views
Distributions with negative support in JAGS
I am creating a Bayesian regression model where I want to include a prior for a variable that can only have a negative coefficient. What distribution can I use that only has a negative support and is ...
- 101
3
votes
1
answer
760
views
How to choose a prior : family for a response with negative values?
I’m modeling percentage change in oxygen levels in the blood from a particular experiment. So my prior before seeing the data was an inverse gaussian distribution. But my data (response variable ) has ...
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 ...
2
votes
1
answer
193
views
Parameters of beta distribution with a given HDI [duplicate]
Is there some way to calculate the parameters of a beta distribution, if the highest density interval is known. That is, given $a,b,x$ I want to have a beta distribution such that the probability of ...
- 2,671
0
votes
0
answers
104
views
Prior Predictive Distribution for hierarchical model
What I need to do is figure out the prior predictive distribution for the following mixed model: $$\begin{align*}
y_{ij} & \sim \mathsf{Normal}(\alpha_j + \beta x_i, \sigma^2)\\
\alpha_j & \...
