# 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.

930 questions
Filter by
Sorted by
Tagged with
3k views

### Prior Gamma distribution: Select appropriate alpha given beta and median

I am trying to programatically select a prior distribution from the Gamma family of distributions. The primary criteria that I need to satisfy is that the median of the distribution should be a given ...
1 vote
351 views

• 325
6k views

### half-cauchy prior for scale parameter

I am looking for a prior for a scale parameter for which I have prior knowledge such that: "$\sigma$ typically does not exceed 100." ("typically" meaning that occasionnally this can happen). In such ...
• 4,673
4k views

### How do I combine multiple prior components and a likelihood?

Lets imagine I am comparing two groups of animals (treatment/control). There is previous data from cell cultures indicating the treatment should have a positive effect. This gives me "prior component ...
• 1,711
1k views

### Why use ${1/\sigma^2}$ as a prior for $\sigma^2$?

In a lot of cases, the prior for $\sigma^2$ is chosen so that it is proportional to ${1/\sigma^2}$. I have a few queries re this: What is the intuition for this choosing this prior? What is the ...
• 51
1k views

### Use the improper prior $p(v) \propto 1/v$ into Jags

I know that one can approximate this density ($p(v) \propto 1/v$) using its truncated version and implement it this way: ...
• 4,673
1 vote
166 views

### MCMC for an explicitly uncomputable prior?

I am trying to sample from a posterior distribution and I only have an explicit formula for likelihood but I can sample from the prior distribution. How can I sample from the posterior distribution ...
• 1,425
1 vote
281 views

### How can I get the prior of a random variable that's a function of a random variable in Bayesian data analysis?

I have a model which includes the following priors: $\lambda_C \rightarrow \dfrac{1}{\sigma_C^2}$ and $\sigma \sim \text{uniform}(0,500)$ Where $\sigma$ is the standard deviation and $\lambda_C$ ...
6k views

### What exactly is weakly informative prior?

Is there a precise definition of weakly informative prior? How is it different from a subjective prior with broad support?
• 1,580
1 vote
82 views

• 13.1k
5k views

### How to specify the Wishart distribution scale matrix

I'm running the below Bayesian mixing model in R using the rjags package, but I am having difficultly in specifying the scale matrix for the Wishart distribution. Essentially, I want Sigma.inv to be a ...
• 71
206 views

### Question about foundations of the uniform shrinkage prior

I am collecting papers about the uniform shrinkage prior for hierarchical Bayesian model. In "A prior for the variance in hierarchical models" of Michael J. Daniels it is stated at the end of page two ...
• 4,673
9k views

### Flat, conjugate, and hyper- priors. What are they?

I am currently reading about Bayesian Methods in Computation Molecular Evolution by Yang. In section 5.2 it talks about priors, and specifically Non-informative/flat/vague/diffuse, conjugate, and ...
• 862
1k views

### Prior selection for Gaussian Processes (GP)

I am trying to select a prior for the covariance parameters of my Gaussian Process (GP) and have been running into numerical problems with my MCMC code. My model is the following: Y = D\beta + GP(... 1 vote
111 views

### Getting Bayes Prior

We want to predict how many points per game LeBron James is going to get per game. Assume there is some underlying theta that does not change game to game, that predicts how many points he will get. ...
• 433
20k views

### How do I choose parameters for my beta prior?

Suppose today I'm going to flip a coin. I believe that 9 of 10 flips will come up heads. I flip the coin and 8 of 10 are heads. Is my distribution of belief beta(9+8, 1+2) beta(1+9+8, 1+1+2) beta(...
• 3,066
195 views

• 186
110 views

### priors for strictly positive index or score types of variables

Is there a prior that's commonly used for "index" or "score" type variables that are user-defined as a weighted sum of a small number of variables (sometimes with pre-defined interaction contributions)...
• 2,524