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Questions tagged [uninformative-prior]

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

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Objective priors for simulator-based models?

I've read a bit about how to derive parametrization-invariant priors for models where we have access to derivatives of the likelihood function and can compute the Fisher Information Matrix: http://www....
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1answer
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Sensibly vague priors for a normal

In the middle of page 64 of the third edition of Bayesian Data Analysis, Gelman writes... We saw in Chapter 2 that a sensibly vague prior for $\mu$ and $\sigma^2$, assuming prior indipendance of ...
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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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What is the interpretation for the priors in the derivation of Laplace smoothing?

Laplace smoothing has a generalisation that can be justified with the use of Bayes formula. Let $f(x;\alpha,\beta)$ be the (non-normalised) beta distribution, i.e. $$f(x;\alpha,\beta) = x^{\alpha-1}(...
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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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Bayesian estimates for Deming regression coinciding with least-squares estimates

Consider the following Deming model with independent replicates : $$x_{i,j} \mid \theta_{i} \sim {\cal N}(\theta_{i}, \gamma_X^2), \quad y_{i,j} \mid \theta_{i} \sim {\cal N}(\alpha+\beta\theta_{i}, \...
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262 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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Understanding my posterior with an uninformative prior with a poisson likelihood. Am I thinking about this correctly?

I have a problem to which I am trying to apply a Bayesian model. My data is generated as follows \begin{align} N_i \mid \mu &\sim \text{Poisson}(\mu) \\ Y_i \mid N_i, \theta_i &\sim \text{...
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109 views

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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22 views

uninformative prior for something dependent on states?

Say I have a model which predicts something say abc over time I define 3 states, S1, S2, S3. I define transition transitional probs. I have another variable say, xyz which has value of 0 to 5. xyz ...
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Understanding the influence of the prior distribution on the original parametrization

Be $y_1,y_2,..y_2$ a simple random sampling from $p(y|\theta)$. Be $\theta$ a parameter with a given prior distribution $p(\theta)$. A way to understand how much informative is $p(\theta)$ is to plot ...
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Is Independent jeffreys prior different from independent reference prior?

I have a model involving two scalar parameters $\theta_1$ and $\theta_2$ and derived the Jeffreys prior for $\theta_1$ and $\theta_2$ independently (so for, e.g. $\pi(\theta_1)$, setting in the ...
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159 views

Stochastic Block Model Priors

In the generic stochastic block model (binary edge data, no degree correction, etc.), if an uninformed prior is used for the Bernoulli coefficients i.e. Beta with $(a,b) = (1,1)$, will the model ...
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138 views

Convenient posterior distribution for homogeneous bivariate Gaussian model

For the model given by some independent pairs $(x_i,y_i)$ identically generated from a bivariate Gaussian distribution, there is the convenient semi-conjugate family of "Normal-Wishart" prior ...
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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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0answers
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Selecting appropriate priors for bayglm with binomial distribution

I've been running a glm with a binomial distribution and two predictors which are date and a categorical variable named 'pond': glm(yes/no ~ date + pond, family=binomial(link="logit"), data=dat) ...
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Bayesian- Can we use uninformative prior for time

I have a doubt about what type of prior to use for time. For example, I am trying to estimate the time in a port. I collected a bunch of data that measures time for a ship to stay in a port, but I do ...
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Bernardo (1979) paper, section 3.2

In section 3.2 of his paper, "Reference Posterior distribution for Bayesian Inference" (on 10 Dec, 2018) he writes $$H(p^*(\theta/z))=-\int p^*(\theta/\hat{\theta})log( p^*(\theta/\hat{\theta}))d\...
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Objective Bayesianism: Jeffreys priors vs reference priors vs principle of transformation groups

According to this answer, José Bernardo has produced an original theory of reference priors where he chooses the prior in order to maximise the information brought by the data by maximising the ...
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Multilevel meta analysis - how to set a uniform prior with boundaries

I am currently conducting a three-level meta-analysis and I would like to run the meta-analysis also by using a Bayesian approach. To run a meta-analysis I collected effect sizes that are correlation ...
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Why can scientists that refuse to bound the prior probability declare discoveries?

Summary: There appears to be scientists that refuse to put prior probabilities on some statements, such as the existence of the Higgs Boson. This is an understandable position. These scientists, ...
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specifying prior distribution for parameter when no prior information alvailable

I am in the middle of finishing my undergraduate thesis which titled "Model Selection Analysis with Bayesian Model Averaging on Logistic Regression". There are some questions that I want to ask you ...
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Reference prior for a three-parameter model and likelihood factorization

Let a (regular) statistical model with three parameters $\phi_1$, $\lambda_2$, $\mu$, and three observations $x_1$, $x_2$, $y$. Assume the likelihood has form $$ L(\mu,\phi_1,\lambda_2 \mid y, x_1, ...
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Non-informative prior for integer restricted parameters

Does anyone have advice/references on choosing a minimally informative prior for the shape parameter of an Erlang distribution (gamma distribution with shape parameter restricted to integer space), or ...
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Non-informative prior for the covariance matrix

I'm currently working on a project around the Bayesian approach to portfolio selection, and I can't manage to wrap my mind around the specification of the non-informative (diffuse) prior. Assuming ...
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26 views

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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19 views

Can a Jeffreys prior be used as an Information maximizing distribution if Information is defined using differential entropy?

I know that a Jeffreys prior is the information maximizing distribution for the statistical channel. However, I want to know if I define mutual information as $$I(x;y)=h(x)-h(x|y)$$ where $h(.)$ is ...
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161 views

Posterior distribution of a multi parameter model

Suppose I have a sample of observations $y = (y_1,y_2, ... ,y_n)$ is drawn from a normal distribution $N(\mu,\sigma^2)$. We are assuming a non-informative prior on $(\mu,\log\sigma)$ i.e; $f(\mu,\...