# 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.

839 questions
Filter by
Sorted by
Tagged with
109 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. ...
18k 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(...
178 views

104 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)...
7k views

### What are typical values to use for alpha and beta in Latent Dirichlet Allocation?

Specifically in the case where I don't know anything about the documents I'm working with. I'm looking a specific number or number range.
293 views

### Help with Bayesian inference in OpenBugs

I have a task that involved Bayesian inference and could use some pointers and hints. I've already got some parts figured out but others remain blurred. Also, my OpenBUGS abilities are frankly limited ...
243 views

### Detect bias in subset of Bernoulli processes

I'm looking for advice on the best method to use to answer this question. General scenario: We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
205k views

### Help me understand Bayesian prior and posterior distributions

In a group of students, there are 2 out of 18 that are left-handed. Find the posterior distribution of left-handed students in the population assuming uninformative prior. Summarize the results. ...
4k views

### Neg Binomial and the Jeffreys' Prior

I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated. Okay, so the situation ...
534 views

### Selecting a Bayes shrinkage prior

I'm looking for a way to integrate prior knowledge about a parameter in a context equivalent to Bayesian hierarchical models. I come from frequentist background and I'm uninitiated in hierarchical ...
94 views

138 views

### A re-formalization of a conjugate prior?

It is quite easy to prove that if $p(\theta)$ is a conjugate prior to some likelihood then the following: $$q(\theta') \propto p(\theta)I(\theta \in A)$$ where $A$ is a subset of the parameter space ...
185 views

### Maximum entropy priors in infinite dimensional spaces

Has the idea of a maximum entropy probability distribution been explored for function spaces, and if so what are some key papers, books, or terms to look for? For $\mathbb{R}^n$ (and discrete spaces),...
23k views

### Why is the Jeffreys prior useful?

I understand that the Jeffreys prior is invariant under re-parameterization. However, what I don't understand is why this property is desired. Why wouldn't you want the prior to change under a change ...
1k views

### Specifying the Form of Prior, Likelihood and Posterior Distributions for Bayesian Analysis

I have recently begun to look into Bayesian Analysis, and, although I'm beginning to get to grips with the general framework (i.e. $\text{posterior} \propto \text{likelihood} \times \text{prior}$), I'...
560 views

### Creating a correlated prior

I would like to create a "weakly informative" prior distribution for a couple parameters. They both could theoretically take any value between 0 and 1, but I have reason to think that they should be ...
7k views

### Parameters without defined priors in Stan

I've just started to learn to use Stan and rstan. Unless I've always been confused about how JAGS/BUGS worked, I thought you always had to define a prior ...
27k views

### Natural interpretation for LDA hyperparameters

Can somebody explain what is the natural interpretation for LDA hyperparameters? ALPHA and BETA are parameters of Dirichlet ...
223 views

### Weighted Distributions in Predictive Model

I'm not a statistician but do work with large datasets and have a problem I'd like to use a predictive model for. I have two datasets that I'd like to use together to build predictions. The first ...
4k views

### Bayes factors with improper priors

I have a question regarding model comparison using Bayes factors. In many cases, statisticians are interested on using a Bayesian approach with improper priors (for example some Jeffreys priors and ...
2k views

### Hyperprior distributions for the parameters (scale matrix and degrees of freedom) of a wishart prior to an inverse covariance matrix

I'm estimating several inverse covariance matrices of a set of measurements across different subpopulations using an wishart prior in jags/rjags/R. Instead of specifying a scale matrix and degrees ...
673 views

### How to specify a non MLE prior for a naiveBayes model in R?

I am just learning R, and am aware that the package e1071 has a naiveBayes method that takes in predictor and class membership, and estimates the class prior using ...
9k views

### How is the inverse gamma distribution related to $n$ and $\sigma$?

Given that the posterior estimate of $\sigma'^{2}$of a normal likelihood and an inverse gamma prior on $\sigma^2$ is: \sigma'^{2}\sim\textrm{IG}\left(\alpha + \frac{n}{2}, \beta +\frac{\sum_{i=1}^n{...
132 views

704 views

### Gamma-normal distribution as prior

When I study the Bayesian econometrics, the book firstly introduces Gamma-Normal distribution as (conjugate) prior, then the posterior will have the same distribution as the prior. But my question is, ...