# 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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### Non-Dirichlet Prior for $Cat(\theta)$ parameter that can tractably be integrated out (for Latent Dirichlet Analysis)?

In LDA Topic Models, it is standard to 'integrate out' the $\theta$ parameter, which contains a document's Categorical probabilities of drawing each topic. QUESTION If one uses the standard Dirichlet ...
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### Bayesian statistics: what is the variable we are integrating in?

This is a screenshot from Bayesian Data Analysis by Gelman. I am a little bit confused by Equation 1.4 (first and second lines), having read Equation 1.3. In Equation 1.3, the variable of integration ...
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### Non-informative prior of a geometric distribution [duplicate]

If we are given a standard geometric distribution $(1-p)^{x-1} p$, with $0<p<1$ what would be a suitable non-informative prior for this?
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### Informative priors for standard deviation (or variance)

Suppose I want to perform Bayesian estimation of the mean $\mu$ and standard deviation $\sigma$ of a Gaussian distribution. Is there a standard way to specify an informative prior over $\sigma$, ...
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### How can I sample from a shifted and scaled Student-t distribution with a specified mean and sd in R?

I'm currently building some Bayesian models with the brms package and the default intercept prior is student_t(3, 0, 6.3) and so ...
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### Can I transform a parameter's posterior to a different parametrization?

I have a model with several parameters. I apply Bayesian inference with a uniform prior for all of the parameters. After the process is finished, I realize that I need one of those parameters $x$ ...
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### Choosing priors for the parameters of Gamma distribution

Suppose that $X_1, X_2, \cdots, X_n$ is a sample drawn from a Gamma distribution with parameter $\alpha$ and $\beta$. Then, the likelihood function can be written as follows: L(\...
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### Why does a GAN generate samples from a random prior?

I've been reading Goodfellow et. al.'s paper on GANs and also the conditional GAN one by Mirza et. al. While relatively straight forward, I'm not sure I understand why the prior for the generator is ...
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### Probability of finding an object on the beach: Bayes theorem [closed]

Introduction Beach litter surveys are collections of observations that detail the object and quantity found of that object within a defined length of shoreline. The sampling protocol was initially ...
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### With knowing the exact form of the prior density, how to improve the convergence/acceptance rate of an independent Metropolis Hasting algorithm?

I have a set of parameters $[\eta_1,\eta_2,...,\eta_k]$ (k can be a bit large, sometimes k=40) to estimate via the Bayesian MCMC method. I know that each component of $\eta_{k}$ is independently ...
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### What prior distribution could one choose to model the number of survey comments?

This question has been inspired by the recent release of the results of a company survey to its employees. There were 12,000 respondents and 16,000 comments. This means that, necessarily, more than ...
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### Exponential Posteriori with a Uniform Prior

I'm studyng for a final exam and found this problem from another generation, but I don't know how I should continue... I will be gratefull for any help, thanks you. Let be $X|\theta\sim U(0,\theta)$ ...
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### Lasso (or Ridge) vs Bayesian MAP

This is the first time I have posted here. I am looking for some feedback or perspective on this question. To make it simple, let's just talk about linear models. We know the MLE solution for the $l_1$...
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### Need help computing and sampling from a posterior distribution

I am trying to compute and draw samples from a posterior distribution. Here is what I have: My data, $\textbf{x}$, is a vectorized $N\times N$ image, i.e. it is of length $N^2$. An arbitrary shape (...
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### Is a draw from the posterior always the same as a draw from the prior?

I'm reading Bayesian data analysis. On page 155, the authors state: Each of the [...] parameters were assigned independent Beta(2, 2) prior distributions. ... If the model were true, we would expect ...
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### Is this Considered "Cheating" in Bayesian Modelling?

Suppose you have some data that corresponds to a single predictor variable and a single response variable. You are interested in fitting a regression model to this data : Y = B_0 + B_1 * X If you ...
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### In Bayesian models, can you use Uniform(-inf, inf) as a prior?

In Bayesian models, can you use Uniform(-inf, inf) as a prior? I ask because in an class, we looked at MH MCMC sampler, and showed that to sample from a distribution, we need not explicitly solve for ...
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### Why Are Empirical Bayes Methods Not Considered "Controversial"? [duplicate]

I was reading about Empirical Bayesian Methods and came across the following: My Question: As this text explains, I have often heard that the priors used in Bayesian Methods should be decided prior ...
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### What kind of bayesian approach should be used for expenditure reasearch?

I must find determinants of expenditure which using baysian approach. Dependent variable: LN education expenditure Independent variables: continuous: LN income, study year of mom, commuting time to ...
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### Data-informed grouping of covariates in Bayesian Hierarchical Modeling?

Is there a way to place a prior on the first stage's betas that allows the second stage groups to be determined from the data? I am working with co-exposures where I am not super confident in how they ...
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### What distribution would make a good hyper-prior for a Beta distribution parameterized by mean and sample size?

I have a model which includes a Beta distribution and I am looking for guidance on how to parameterize a hyper-prior for it. For example, this post uses a Beta parameterized with a mean and ...
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### What does the beta parameter tell you in the cauchy distribution?

I am doing some bayesian analysis, and I recently used the half-cauchy distribution as a prior for a variable that tracked monthly spending. My thinking is that this is a non-negative number that is ...
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### How to set prior for Bayesian analysis

I am new to statistics and Bayesian analysis. Therefore, I have some problems that would like to clarify. Suppose my problem is to calculate the posterior distribution for the time of ship to spend in ...
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### Choosing informative Gibbs priors for Bayesian updating

I'm trying to create some kind of iterative Bayesian algorithm, which continuously updates as more data is gathered. The aim is to iteratively update the coefficients based on the second dataset using ...
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### Bayes prior in MAP estimation corresponding to $\ell^0$ penalization

I gather that in the context of penalized least squares, we can interpret a penalty term as corresponding to a prior $\pi(\beta)\propto \exp\{-\text{pen}\}.$ Is this also true for $\ell^0$ ...
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### Bayesian priors associated with regularization penalties

I gather that adding a penalty term to (linear) least squares minimization typically corresponds with choosing some prior for Bayes estimation in the normal linear regression model. A couple questions ...
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