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.
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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. ...
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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 ...
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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 ...
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Eliciting priors from experts
How should I elicit prior distributions from experts when fitting a Bayesian model?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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How to choose prior in Bayesian parameter estimation
I know 3 methods to do parameter estimation, ML, MAP and Bayes approach. And for MAP and Bayes approach, we need to pick priors for parameters, right?
Say I have this model $p(x|\alpha,\beta)$, in ...
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