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 point of using an uninformative prior distribution? [duplicate]

If I am completely unknowing as to the true value of $\theta$ in some parameter space $\Theta$, why would I use a flat prior distribution when all the information about $\theta$ will be in my sample? ...
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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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36 views

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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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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27 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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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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300 views

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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1answer
59 views

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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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': ...
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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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123 views

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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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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Why are weakly informative priors a good idea?

There are many solutions to the problem that typically not enough information is available to fully specify a prior. For all approaches (I know) but weakly informative priors I kind of understand ...
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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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34 views

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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59 views

Better skill checks for RPGs - Conditional probability given 2 independent parameters

I am trying to find a better way (theoretically, not practically speaking) to do a skill check for a Skill Trial in RPGs. In several RPGs, a skill check consists of a Playing Character (PC) trying to ...
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1answer
61 views

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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249 views

How to quantify strength of beta prior?

How would one interpret the strength of prior belief associated with a parameter with a prior beta(10,8) distribution, compared to a beta(0,0) prior, (with data from a binomial distribution)? Some ...
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818 views

Prior comparison: Uninformative vs informative

I have a question about prior choice that has arisen from some analysis I have been doing. I don't think the particular details of the model are necessary for this question, but my Bayesian knowledge ...
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Haldane's prior Beta(0,0) - Part 1

This article$^1$ on p.16 specifies Haldane's prior as: $$p(\theta) = \frac{1}{θ(1−θ)}$$. However, other$^2$ source on p.6 specifies Haldane's prior as proportional to $\frac{1}{θ(1−θ)}$, i.e. $$p(\...
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408 views

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 ...
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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 ...
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354 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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767 views

noninformative prior (normal data)

Can someone help me through the derivation? That is, how is summation of (yi-mu)^2 equal to the equation that follows? where did n(y(bar)-mu)^2 come from? Thanks.
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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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182 views

Specification of priors for multivariet hierarchical regression using MCMCglmm

I'm analyzing data from experiment, where people had to select a point in plane. I'm trying to asses which atributes of the task and personality are asociated with the outcome. Becouse we used ...
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201 views

Bayesian Biased Prior Formula

I know that for a Bayesian uniform/flat prior, the formula is 1/n (and n=1), as each value has an equal chance of being chosen. However, is there an equation for when the prior is biased/informative? ...
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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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375 views

Uninformative (flat) Prior density for non-linear functions [duplicate]

We, bayesians, usually use non-informative priors for the parameters like $p(\beta)\propto 1$. Someone told me that such a flat prior is informative to some extent for non-linear functions of the ...
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350 views

What is the bayesian uninformative exponential prior?

I am looking to model a poisson process $X \sim Poisson(\lambda)$ and infer $\lambda$ using bayesian inference from $X$ e.g. $[0,0,0,2,1,0,0,2,1]$ could be my dataset. The data comes from the count of ...
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162 views

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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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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Understanding the Proof for why Jeffreys' prior is invariant

I was reviewing the section of Andrew Gelman's "Bayesian Data Analysis" on uninformative priors, and came across this explanation for why Jeffreys' prior is invariant to parameterization. My question ...
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186 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,\...
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Prior distribution importance in Bayesian inference

I am performing a Bayesian multivariate regression, and therefore I have to construct the prior and the subsequent posterior. But the paper that I am using as a reference, uses a "Uninformative prior"...
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149 views

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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1answer
523 views

Why is Inverted Gamma (3,0.0005) a diffuse prior when variance of this random variable is small?

A few times I came across the statement that an Inverted Gamma (3, 0.0005) prior for the variance is quite diffuse but proper. Hence, my understanding is that the prior variance of this random ...
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1answer
517 views

Bayesian estimate of the parameter of a truncated Poisson distribution (using R)

Suppose that I am working with an integer-valued variable $x$ and that all I know about my sample is as follows: Mean $\bar{x}$: 4.5 Sample size $n$: 100 I can safely assume that the underlying model ...
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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 ...