Questions tagged [uninformative-prior]
A prior that express lack of detailed information or lack of any information at all.
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What is the advantage of running generalized mixed effect linear regression model with bayesian with non-informative prior vs frequentist approach?
I am curious as to whether the bayesian approach with non-informative prior (flat prior) is more suitable for generalized mixed effects linear model than frequentist approach and what the reasons may ...
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In Bayesian modelling how to interpret hierarchical hyperparameters with regards to "borrowing"?
With regards to hierarchical models I often see these referred to as groups borrowing information from each other e.g.
It will be seen that the hierarchical model posterior estimates for one school ...
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What is the right Haar prior for the Weibull distribution?
From Wikipedia, the Weibull distribution is defined with the exceedance distribution function (aka survival function) $\exp[-(x/\lambda)^k]$.
If I transform the random variable $x$ using $x'=ax^b$ ...
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Informative priors for Bayesian chi-squared test
A colleague recently presented results from a chi-squared test that used a Bayesian method for estimation. The results seemed promising, but when I looked up the main function ...
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How can I solve identifiability problems in my STAN estimation?
So I am trying to validate my STAN model before using real data and am having some trouble estimating parameters separately. My data structure contains count data with people on the rows, and test ...
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Distribution families whose likelihoods integrate to $+\infty$ for some sample values
I've recently started learning about Bayesian statistics, and I came across this very nice answer by Xi'an https://stats.stackexchange.com/a/129908/268693, which [in my slight paraphrasing] says the ...
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Quantiles of the posterior predictive distribution of a Gumbel random variable under the degenerate prior $\pi(\mu,\sigma) = \sigma^{-1}$
I need to find an automatic way to calculate with good precision the quantile of the posterior predictive distribution (ppd) of a random variable following a Gumbel law, under the degenerate prior $\...
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Creating half normal probability distribution
I have come across a problem where a half normal distribution is based on a single number, namely the sum of all costs. The exact definition of the number is not important. The important think is that ...
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Distribution of the sample variance given that $\sigma^2$ is unknown
By Cochran's theorem, if $y_1,....,y_n\sim\mathcal{N}\left(0,\sigma^2\right)$ independently with a known variance $\sigma^2\in\mathbb{R}_{>0}$, then
\begin{equation}
(n-1)\frac{S^2}{\sigma^2}\sim\...
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Bayesian Analysis in the Absence of Prior Information?
I have always wondered - how confident do researchers tend to be in their "prior" information when deciding to create statistical models using a Bayesian Approach vs. a Frequentist Approach?
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Bayesian replication, but with new variables
Suppose I have data I've collected containing predictor variables $X_1, X_2$, and $X_3$. I build a main effects statistical model predicting $Y$ from these predictors and estimate the relevant ...
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Noninformative prior for Gaussian precision as the special case of Gamma distribution with both parameters being zero
The question is from page 120 of book "Pattern Recognition and Machine Learning" by Christopher M. Bishop. I excerpt it as follows:
The definition of gamma distribution $\textrm{Gam}(\...
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Is there any strong argument about objective/non-informative improper prior?
Decades ago improper objective priors - e.g. $\pi(\sigma) \propto \sigma^{-1}, \sigma > 0,$ for a scale parameter - were considered problematic because some authors thought they were leading to the ...
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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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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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Literature on Noninformative Priors for GPD
I am starting to do some work using the Generalized Pareto Distribution (GPD), and was hoping someone might be able to point me in the direction of literature (or just general recommendations) on ...
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Is it really worth doing Bayesian Analysis if you have no idea about Priors? [duplicate]
I have heard that if you use uniform priors in Bayesian Analysis, it is the same as doing Frequentist Analysis. If you are creating statistical models and you really have no idea about the prior ...
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Are there any uninformative priors with an unlimited support like $(-\infty,\infty), (0,\infty), (-\infty,0)$? [duplicate]
The Bayes theorem is:
$P(\theta | x)=\displaystyle \frac{p(\theta)L_x(\theta)}{\int_{\theta \in A}p(\theta)L_x(\theta)d\theta}$
It's pretty clear that $\theta's$ support will not change as bayes ...
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Analytical expression of the log-likelihood of the Binomial model with unknown $n$ and known $y$ and $p$ and its conjugate prior
I'm trying to derive the MLE and Bayesian posterior for $n$ in the Binomial model, $\mathrm{Binomial}(n, p)$ with known $y$ and $p$. The following questions arise
How to derive analytically the ...
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Batches of bayesian updates for gaussian with unknown variance different from computation with all data
I'm working on a project where I continuously (in batches) update the pdf estimation for an event normally distributed. My variance is unknown, so I'm using the equations given in session 4.1.2 of ...
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How does one place an uninformative prior on a Gamma Distribution?
I'd like to choose an uninformative prior for the scale and shape parameters of the Gamma distribution. Any help and suggestions will be appreciated.
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Why is Cauchy the default prior for both testing and estimation?
Assume that a data set follows a normal distribution and the prior and posterior both have a normal-gamma distribution. When we are performing Bayesian analysis but don't want any subjective choice of ...
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Numbers of draws on a modified Bernouilli process
Here is the setup:
Bob runs an experiment: he flips a coin N times (between 0 and +$\infty$). The coin has a probability p of landing on heads. Bob starts with zero points. For each head, Bob scores a ...
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When can a winner of the election be called: estimating population proportion without the assumption of random sampling
While following a recent election, I wanted to estimate population proportion of people who voted for a certain candidate knowing the sample proportion, sample size (and population size).
I first ...
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Bayes Estimate for Mean Squared Loss in Uniform Prior
Can some one please help me out in Verifying if my prior distribution is uniform then will my Bayes estimate will always be MLE or UMVUE?
If $X_i$ follow iid $N(\theta,1)$ and prior distribution of $\...
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Non-informative prior for Exponential
I am working with a Bayesian model: $T \sim exp(\theta)$ for survival data, I have chosen a gamma distribution as a prior since its conjugate by an exponential distribution. I'd like to choose a $\...
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Choosing reasonable priors for Poisson GLMM
I am using the package brms in R to fit a generalized linear mixed model using a Poisson distribution with log link.
The model takes count data that ranges from 0 ...
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What is a non-informative choice of parameters for a Dirichlet distribution?
Dirichlet distribution is a conjugate prior for multinomial distribution. I want to impose a non-informative prior over sampling weights $\pi$ for a draw $x=(x_1,…,x_N)$ from a multinomial ...
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Uniform posterior on bounded space [duplicate]
In a particular Bayesian problem, I have encountered a choice of parameters that leads to a uniform posterior distribution. Given prior
\begin{equation}
p(\boldsymbol{\pi}) =Dirichlet(\boldsymbol{\...
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How to choose a non-informative or weakly informative hyper priors for my hierarchical bayesian model?
I am learning Bayes on "Applied Bayesian Statistics" by MK Cowles.
The chapter about "Bayesian Hierarchical Models" mentioned an example that we estimate a softball player’s ...
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Why is this an example of a noninformative prior?
From Bayesian Data Analysis 3rd Edition [Gelman et. al], they give this as an example when introducing non-informative priors:
"We return to the problem of estimating the mean θ of a normal ...
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location/scale invariant priors
I'm trying to understand what's the motivation behind these priors, and why they are used.
I understand that for location parameters of some distribution, you want it to be invariant of movement. e.g....
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Setting priors for bivariate regression
I would like to perform a bivariate MCMC regression with boldness scores as the continuous response variable, aggression ranks as the ordinal response variable, trial numbers as fixed effect and ...
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Choosing a ‘noninformative’ hyperprior distribution
I am trying to better understand hierarchical Bayesian models.
I started here: https://blog.dominodatalab.com/ab-testing-with-hierarchical-models-in-python/
And ran into the following sentence ...
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Jeffreys prior vs. Flat prior on $(\beta,\log\sigma^2)$
I'm reading Bayesian Core, and the authors state that a Jeffreys prior $\pi(\beta,\sigma^2|X)\propto\frac{1}{\sigma^2}$ corresponds to a flat prior on $(\beta,\log\sigma^2)$. Why is this so?
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Can an improper prior distribution be informative?
I have just worked through an example where, with an improper prior, the bayesian estimator equals the maximum likelihood estimator, leading me to believe that improper priors are uninformative. But ...
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Maximum entropy prior for dichotomous variables [closed]
I have a set of dichotomous variables $A, B, C,$... and I know their probabilities $P(A), P(B), P(C),$... as well es their pairwise dependencies $P(A \cap B), P(A \cap C), P(B \cap C),$... . Or in ...
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Justification for specifying the parameters of prior mean distribution in stochastic volatility
In a paper about the stochastic volatility, the author justifies his choice of prior distribution parameters $\pi(\mu) \sim \mathcal{N}(b_\mu,B_\mu) = \mathcal{N}(-9,0)$ of the level $\mu$ as follows:
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$X\sim \mathcal{N}(\theta,\sigma^2)$, $\pi(\theta,\sigma^2)\propto 1/\sigma^2$, $Y\sim \mathcal{N}(\rho X,\sigma^2)$, $\rho$ fixed. $f(y|x)$?
like in the title I have the following question.
Let $X\sim \mathcal{N}(\theta,\sigma^2)$ with the improper prior $\pi(\theta,\sigma^2)\propto 1/\sigma^2$ and consider $Y\sim \mathcal{N}(\rho X,\...
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Quantifying a reduction in prior uncertainty over several experiments
I am interested in how to quantify reductions in uncertainty about the size of an experimental effect over a series of studies which, for hypothetical reasons, preclude the merging of data. I would ...
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Maximum entropy prior for r.v. supported on real line with no other constraints?
What would be a suitable maximum entropy prior for a random variable supported on the real line with no other constraints (i.e. unknown mean, unknown variance, unknown bounds)?
All kinds of answers (...
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Significance of parameterisation invariance of Jeffreys prior
I often hear it said that the Jeffreys prior is well-motivated because it is invariant under reparametrization. The proof of this is quite straight-forward (I know the proof on e.g., wiki). I'm a bit ...
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How do Bayesian hierarchical models adaptively learn the prior?
It seems the main difference between a hierarchical and a non hierarchical model is that the hierarchical model learns the prior. That is it adaptively comes up with a regularizing prior to be applied ...
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How to set a Bayesian prior on a set with a large but unknown number of elements?
Let us suppose that we are trying to analyze a given starfish. We would like to know which species does the starfish belong to. We have a list of 1000 starfish species, but we know that there is an ...
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Are there situations where improper priors can be avoided via a prior on a subset of the real line and a transformation?
There are many situations where improper priors are "permissable" (Berger, 2009). In many cases, these improper priors are improper because they are "flat" on the real line. A well known example is ...
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does Informativeness of the prior always decreases similarity of the posterior mean to the data mean? [closed]
I am looking for a proof of the statement "If the variance of the prior distribution is greater, the posterior is more affected by the data".
More specifically, if X, X' are priors such that E(X)=E(X'...
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Understanding definition of informative and uninformative prior distribution
When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$
Where is the no information for the ...
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Information about parameters using priors distributions [duplicate]
When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$
Where is the no information for the ...
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What would be an ignorance prior of AB, given the probabilities of A and B?
Let us have two events, $A$ and $B$ whose probabilities are $P(A)$ and $P(B)$. In the absence of any other information, what would be a reasonable probability to assign to $AB$, that is, $A$ and $B$ ...
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