# 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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### Horseshoe priors and random slope/intercept regressions

I'm interested in using the horseshoe prior (or the related hierarchical-shrinkage family of priors) for regression coefficients of a traditional multilevel regression (e.g., random slopes/intercepts)....
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### Implementing Predictive Posterior Distribution Using Stan

Background I had an example that sought to demonstrate the posterior predictive distribution in the context of a normal measurement model. The data that was used is as follows: ...
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### Hyper-prior for negative binomial in hierarchical model using JAGS/BUGS

Below I'm using a negative binomial because it is more flexible than a simple poisson model. The data are counts $y$ of events for 16 individuals $x$. There are 14 counts (i.e. counting periods) for ...
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### Including feature-dependent priors on output class, in bayesian logistic regression

When doing logistic regression with data $D_N = \{(x_i, y_i)\}_i^N$ with $x_i \in \mathbf{X}^N$ (each data point has N features) and $y_i \in \mathbf{Y}$ being assigned output classes, in a Bayesian ...
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### Deriving priors for MCMC implementation

I have been working on an assignment lately wherein the object is to implement an MCMC approach to simulate from a generated posterior distribution. The posterior distribution is generated from a ...
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### Reproducing a didactic example of Lindley (1993)

Lindley (1993) discusses the following mixed discrete and continuous prior for the tea tasting lady experiment, where $\pi$ is probability of a correct classification: $p(\pi=0.5) = 0.8$ (discrete ...
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### Bayes-Poincaré solution to k-sample tests for comparison and the Behrens-Fisher problem?

I’d like to share and submit for (dis)approval and discussion yet another, simple but original (to the best of my knowledge) Bayesian solution to the classical problem of comparing k samples or groups,... 121 views

### How to prove that the prior for which Bayes rule is also the minimax rule, is the least favorable prior?

I have read in the book Mathematical Statistics: A Decision Theoretic Approach by Thomas Ferguson that The prior for which the Bayes rule is also minimax rule, then that prior is Least favorable prior....
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### Can someone provide a non-technical explanation of how Cholesky Covariance priors work?

I am looking for an explanation of how Cholesky Covariance priors work in the context of mixed effects regression. In particular, when they are applied to the correlations among random effects. What ...
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### Using Bayesian Lasso with an informed prior

I'm looking for advice on how best to go about setting an informative prior for the Bayesian Lasso and BART (I'm applying these in R using the rjags and bartMachine packages) I have 3 proteomics ...
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### Intuition regarding Bayesian pseudo-priors

One approach to model comparison in a Bayesian framework uses a Bernoulli indicator variable to indicate which of two models is likely to be the "true model". When applying MCMC-based tools for ...
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### Specifying the priors for multivariate MCMCglmm mixed model in R (Poisson distribution)

I am trying to build a model using MCMCglmm. Ideally, I would use a negative binomial distribution for my response; however, this is not an option in MCMCglmm. I don't know of any open-source ...
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### Linear regression with prior on $\arctan \beta_1$

Suppose we have $\hat{y} = \beta_1 x + \beta_0$ (I ask only for the univariate case.) A typical Bayesian approach might involve Normal priors on both parameters. I was thinking today about a ...
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### How to use information about likelihood of classes in a classifier?

General question: How can information about the likelihood of classes be used to improve a classifier? Suppose that the probability of each class is known quite precisely (from a very large sample), ...
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### Haar prior for von Mises distribution

Ok, Let me tell you that this is the very first time that I have no idea with the question below. I can not find a solution or anything that will lead me to it. I say this to prevent comments "what ...
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### 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),...
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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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### Metrics for assessing the quality of prior distributions

Clarification: My purpose is to compare different methods for selecting/creating priors (or perhaps I should refer to them as predictive distributions for a quantity of interest/parameter). I do not ...
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### Least favorable prior - Find the distribution that maximizes the Bayes risk

Suppose I've found that the Bayes risk is of the form $$r(\theta) = \int_{-a}^a \theta^2 \pi(\theta)d\theta$$ I want to show that the following distribution, $\pi(a)=\pi(-a)=0.5$, maximizes this ...
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### How do I choose a prior for this hierarchical model? (Kruschke book)

I am working through Kruschke's "Doing Bayesian Data Analysis", currently working on the Hierarchical models chapter. The book uses JAGS for MCMC. One of the exercises asks the reader to compare two ...
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### Informative priors from frequentist regression

Say I run a standard frequentist regression on a subset of my data (for example using lm in R) and obtain some values for the coefficients of the model, I have fairly large data set ~100k samples. Now ...
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