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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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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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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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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Bayesian prior over long probability vectors
Suppose you have i.i.d. variables $x_i$ in ${1,\ldots,K}$ modeled as
$$P(x_i = k) = \theta_k$$
and and you want to infer the probability vector $\theta$. A Bayesian approach puts a prior over $\...
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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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Why are $\mathbb{E}( \ln(x))$ and $\mathbb{E} ( \ln(1 - x))$ reasonable descriptions of knowledge about a beta distribution?
The max entropy philosophy states that given some constraints on the prior, we should choose the prior that is maximum entropy subject to those constraints.
I know that the Beta($\alpha, \beta$) is ...
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Prior for $\lambda$ is LASSO prior?
I have a regression model with regression coefficients $\beta_j$, $j=1,...,n$, and I would like to use a LASSO prior for $\beta_j$, this is:
$$\beta_j \sim Laplace(0,1/\lambda),$$
where the Laplace ...
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Combining non-independent priors
I've been working on a stats package that includes Bayesian survival models. The user is allowed to write priors directly for all the parameters involved. However, I think it's pretty difficult for ...
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Examples of usage of community of priors or why aren't they used more commonly?
Kass and Greenhouse (1989) proposed using "community of priors" (see also Fayers et al, 1997; 2000). As described by Spiegelhalter (2004), they can be seen as a
range of viewpoints that should be ...
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Noninformative prior for variance, understanding and coding
I have three questions regarding the understanding behind and implementation of a noninformative prior for variance. I'm attempting to build a Metropolis sampler and I'm trying to sample from a ...
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AR(1) model - which prior to use?
I want to use the following univariate model:
$y_t = \mu_t + \epsilon_t, \ \epsilon_t \sim N(0,1)$
$\mu_t = \phi \mu_{t-1} + \omega_t, \ \omega_t \sim N(0,\sigma_\omega^2)$
That is, $\mu_t$ follows ...
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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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Prior elicitation with Normal-Gamma or Normal-Inverse-Gamma
I am looking for a way to have experts elicit a prior for a Normal-Inverse-Gamma Bayesian linear regression model. Is there any material suggesting intuitive ways to go about this?
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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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