# 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.

830 questions
Filter by
Sorted by
Tagged with
203k 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. ...
31k views

### What is an “uninformative prior”? Can we ever have one with truly no information?

Inspired by a comment from this question: What do we consider "uninformative" in a prior - and what information is still contained in a supposedly uninformative prior? I generally see the prior in ...
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 ...
5k views

### Eliciting priors from experts

How should I elicit prior distributions from experts when fitting a Bayesian model?
6k views

### Why would someone use a Bayesian approach with a 'noninformative' improper prior instead of the classical approach?

If the interest is merely estimating the parameters of a model (pointwise and/or interval estimation) and the prior information is not reliable, weak, (I know this is a bit vague but I am trying to ...
5k views

### If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?

I'm very new to Bayesian statistics, and this may be a silly question. Nevertheless: Consider a credible interval with a prior that specifies a uniform distribution. For example, from 0 to 1, where 0 ...
18k views

### Why is Laplace prior producing sparse solutions?

I was looking through the literature on regularization, and often see paragraphs that links L2 regulatization with Gaussian prior, and L1 with Laplace centered on zero. I know how these priors look ...
8k views

### Do Bayesian priors become irrelevant with large sample size?

When performing Bayesian inference, we operate by maximizing our likelihood function in combination with the priors we have about the parameters. Because the log-likelihood is more convenient, we ...
20k views

### What are the properties of a half Cauchy distribution?

I am currently working on a problem, where I need to develop a Markov chain Monte Carlo (MCMC) algorithm for a state space model. To be able to solve the problem, I have been given the following ...
12k views

### Why is Lasso penalty equivalent to the double exponential (Laplace) prior?

I have read in a number of references that the Lasso estimate for the regression parameter vector $B$ is equivalent to the posterior mode of $B$ in which the prior distribution for each $B_i$ is a ...
5k views

### Why are Jeffreys priors considered noninformative?

Consider a Jeffreys prior where $p(\theta) \propto \sqrt{|i(\theta)|}$, where $i$ is the Fisher information. I keep seeing this prior being mentioned as a uninformative prior, but I never saw an ...
10k views

### Is a vague prior the same as a non-informative prior?

This is a question about terminology. Is a "vague prior" the same as a non-informative prior, or is there some difference between the two? My impression is that they are same (from looking up vague ...
7k views

### Bayesian batting average prior

I wanted to ask a question inspired by an excellent answer to the query about the intuition for the beta distribution. I wanted to get a better understanding of the derivation for the prior ...
14k views

### How can an improper prior lead to a proper posterior distribution?

We know that in the case of a proper prior distribution, $P(\theta \mid X) = \dfrac{P(X \mid \theta)P(\theta)}{P(X)}$ $\propto P(X \mid \theta)P(\theta)$. The usual justification for this step is ...
1k views

### History of uninformative prior theory

I am writing a short theoretical essay for a Bayesian Statistics course (in an Economics M.Sc.) on uninformative priors and I am trying to understand which are the steps in the development of this ...
6k views

### Weakly informative prior distributions for scale parameters

I have been using log normal distributions as prior distributions for scale parameters (for normal distributions, t distributions etc.) when I have a rough idea about what the scale should be, but ...
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 ...
11k views

### Why is a $p(\sigma^2)\sim\text{IG(0.001, 0.001)}$ prior on variance considered weak?

Background One of the most commonly used weak prior on variance is the inverse-gamma with parameters $\alpha =0.001, \beta=0.001$ (Gelman 2006). However, this distribution has a 90%CI of ...
2k views

### What is/are the implicit priors in frequentist statistics?

I've heard the notion that Jaynes claims frequentists operate with an "implicit prior". What is or are these implicit priors? Does this mean frequentist models are all special cases of Bayesian ...
4k views

### Posterior very different to prior and likelihood

If the prior and the likelihood are very different from each other, then sometimes a situation occurs where the posterior is similar to neither of them. See for example this picture, which uses normal ...
6k views

### What is the relationship between sample size and the influence of prior on posterior?

If we have a small sample size, will the prior distribution influence the posterior distribution a lot?
10k views

### Choosing between uninformative beta priors

I am looking for uninformative priors for beta distribution to work with a binomial process (Hit/Miss). At first I thought about using $\alpha=1, \beta=1$ that generate an uniform PDF, or Jeffrey ...
3k views

418 views

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 ...
4k views

### What is a “Unit Information Prior”?

I've been reading Wagenmakers (2007) A practical solution to the pervasive problem of p values. I'm intrigued by the conversion of BIC values into Bayes factors and probabilities. However, so far I ...