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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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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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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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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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106 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
47 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': 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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1answer
40 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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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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1answer
37 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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1answer
175 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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1answer
528 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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2answers
738 views

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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1answer
288 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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1answer
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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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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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1answer
649 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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4k views

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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1answer
130 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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1answer
99 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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1answer
286 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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1answer
265 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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152 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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1answer
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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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1answer
747 views

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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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,\...
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3answers
764 views

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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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
392 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
398 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 ...
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1answer
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Laplace's law of succession using different priors

Laplace's law of succession is a well-known rule, relying on Bayes' theorem. A possible proof of the rule of succession can be found on Wikipedia. Note that for this proof we use a uniform ...
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1answer
2k views

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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1answer
522 views

Posterior distribution for Gamma scale parameter under the Jeffreys prior

What is the posterior distribution for parameter $b$ with $X \sim Gamma(a,b)$, under the Jeffreys prior? We can assume that $a$ is known. The Jeffreys prior is the square of the Fisher information ...
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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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What should an uninformative prior be for the slope when doing linear regression?

When performing bayesian linear regression, one needs to assign a prior for the slope $a$ and intercept $b$. Since $b$ is a location parameter it makes sense to assign an uniform prior; however, it ...
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1answer
358 views

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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2answers
154 views

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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1answer
745 views

What is a good example of a non-informative prior for the uniform distribution?

I recently noticed that for non-informative priors, people usually use something like a uniform prior, which works for many different distributions. However, assuming that your likelihood is nothing ...
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1answer
693 views

Priors for Truncated Parameters - RJAGS

I would like to estimate the parameters of a specific model. The model specification is as follows: $p_t = k_t + B_t/(1-B_t) + \eta_t$, where $ \eta_t \sim N(0, \sigma^2)$ $R_{t+1} = R_{t} + R_t (...