# 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 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 ...
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### Marginal prior distribution with restricted parameters

I'm analysing one paper on bayesian inference for network reliability and got stuck at trying to validate some (quite simple at first sight) formulas. Suppose the probabilities of failure has ...
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### Deriving posterior of Beta distribution

You test a classifier on a test set consisting of 10 iid items. The classifier makes 2 mistakes. Assume the true error rate is $x$. Let the prior be $x \sim Beta(\alpha, \beta)$. Derive the ...
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### What prior distributions are used in mcmcsamp() from lme4?

The mcmcsamp() function generates simulations from the posterior distributions of a Bayesian mixed model fitted with the lmer() ...
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### Softmax regression bias and prior probabilities for unequal classes

I'm using Softmax regression for a multi-class classification problem. I don't have equal prior probabilities for each of the classes. I know from Logistic Regression (softmax regression with 2 ...
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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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### Prior of multivariate Polya distribution?

Anyone knows a prior (preferably conjugate) to the multivariate Polya distribution? I need it for Gibbs sampling. So if anyone has another idea, I am interested.
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### How can the F distribution be used, other than for hypothesis testing and confidence interval estimation?

I am trying to fit informed prior distributions to data using MLE, and F occasionally provides a best fit (lowest AIC value). I am starting with only very basic knowledge of probability theory, so I ...
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### What are the modeling approaches in this cartoon?

What are the modeling approaches depicted here? Can you name them and their prominent proponents or a landmark model? Is there an accepted superior approach? Who prefers which approach? (From: http://...
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### Computing ridge regression with prior different from 0

I compute ridge regression results with Matlab, not using their implementation but simply computing (trans(X)X)+kI)^-1+trans(X)y as seen here. The given formula ...
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### Allow data to dictate the priors and then run the model using these priors? (e.g., data-driven priors from same data set)

It is my understanding that we should not be allowing the same data set we are analyzing to drive/define what the prior distributions look like in a Bayesian analysis. Specifically, it is ...
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### Selection of priors for a BYM spatial regression model

I am using a BYM model in WinBugs to describe the distribution of a non-infectious disease. The model at present is a standard enough BYM model without much modification, (a Poisson-gamma hierarchical ...
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### What methods can be used to specify priors from data?

Background I am generally interested in learning appropriate methods of using data to specify priors. A previous question asks how to elicit priors from experts and received some good recommendations....
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### Specifying conditional probabilities in hybrid Bayesian networks

I am trying to get a deeper understanding of the various types of Bayesian networks. Most of the literature/lectures I've come across use discrete random variables exclusively and only mention ...