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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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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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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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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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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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 ...
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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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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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Eliciting priors from experts
How should I elicit prior distributions from experts when fitting a Bayesian model?
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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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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 ...
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How do I complete the square with normal likelihood and normal prior?
How do I complete the square from the point I have left off at, and is this correct so far?
I have a normal prior for $\beta$ of the form $p(\beta|\sigma^2)\sim \mathcal{N}(0,\sigma^2V)$, to get:
$...
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How to define prior for beta-binomial A/B test
I would like to run an A/B test using a Bayesian beta-binomial model whereby I would state probabilities such as $P(p_B>p_A)$ in place of using a traditional T-test. I've read that the prior should ...
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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 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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What is the statistical model for a multi-label problem?
In a setting with a binary $y$ like dog/cat, a reasonable statistical model is to posit that the probability parameter $p$ of a $\text{Binomial}(1, 0)$ distribution is some function $f$ of features $X$...
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