Questions tagged [uninformative-prior]

A prior that express lack of detailed information or lack of any information at all.

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Choosing between uninformative beta priors

I am looking for uninformative priors for beta distribution to work with a binomial process (Hit/Miss). At first I thought about using $\alpha=1, \beta=1$ that generate an uniform PDF, or Jeffrey ...
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Why is Zellner's g prior “unacceptable”?

I know Zellner's prior is using data in order to set prior information, but actually the whole model depends on the data. Is there any other reason?
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What is the mathematical difference between using a un-informative prior and a frequentist approach?

Un-informative priors are preferred in instances where bias is not acceptable (ie. courtrooms, etc.) However, it seems to me that it would just make sense to use a frequentist approach instead. Why ...
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Deriving the posterior density for a lognormal likelihood and Jeffreys's prior

The likelihood function of a lognormal distribution is: $f(x; \mu, \sigma) \propto \prod_{i_1}^n \frac{1}{\sigma x_i} \exp \left ( - \frac{(\ln{x_i} - \mu)^2}{2 \sigma^2} \right )$ and Jeffreys's ...
598 views

Choosing non-informative priors

I am working on a model relying on an ugly parametrized function acting as a calibration function on a part of the model. Using a Bayesian setting, I need to get non-informative priors for the ...
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Downsides of inverse Wishart prior in hierarchical models

I am working with a Bayesian hierarchical model that has a number of parameters for each experimental unit (6 parameters). I really do not know all that much about them a-priori, but it is quite ...
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Why is uniform prior on log(x) equal to 1/x prior on x?

I'm trying to understand Jeffreys prior. One application is for 'scale' variables like the standard deviation $\sigma$ (or its square, the variance $\sigma^2$) of Gaussian distributions. It is often ...
551 views

How does one interpret the distribution over parameters in bayesian estimation?

I am new to Bayesian estimation. The assumption that the parameters are random variables seems a little unsettling to me. For example when considering a model for data, what physical interpretation ...
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Properties of MaxEnt posterior distribution for a die with prescribed average

Question: after throwing a die a large number of times and discovering that the average of the outcomes is $4$, what probability distribution one should assign to statements "the next roll will be $i$"...
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How to construct “reference priors”?

I have been reading about noninformative priors. Two of the most popular priors of this kind seem to be the Jeffreys prior and the reference prior. The Jeffreys prior has a clear construction, being ...
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Issues with Importance sampling for flat prior

I am trying to draw Bayesian inference via importance sampling for a parameter $\xi$ attached with an (unbounded) flat prior. This seems problematic as this is clearly not a probability measure but ...
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Non-informative prior for regression model

I'm looking at p. 355 of Gelman's Bayesian Data Analysis (3rd ed.), for which there is no errata, and I see this: In the normal regression model, a convenient non-informative prior distribution ...
327 views

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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Forecasting with no prior knowledge - Bayesian vs Frequentist

I have a basic question about Bayesian statistics. Lets say that I want to make forecasts of a certain response variable, based on explanatory variables and lagged responses variables, while I have ...