Questions tagged [uninformative-prior]

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

Filter by
Sorted by
Tagged with
12
votes
2answers
549 views

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 ...
0
votes
0answers
8 views

What kind of bayesian approach should be used for expenditure reasearch?

I must find determinants of expenditure which using baysian approach. Dependent variable: LN education expenditure Independent variables: continuous: LN income, study year of mom, commuting time to ...
0
votes
0answers
13 views

EM (?) algorithm with dependent observations but the prior seems not informative

How can we derive the (EM?) algorithm to estimate $b$ if we suppose $G_j = bg_j$ for all $j$, the priors (?) of the observations $\hat{G}_j \sim N(\hat{G}_j | G_j, (s_{G, j})^2)$, $\hat{g}_j \sim N(\...
1
vote
0answers
76 views

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 ...
3
votes
4answers
100 views

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 ...
0
votes
0answers
17 views

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 ...
4
votes
1answer
153 views

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 ...
1
vote
1answer
72 views

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 ...
1
vote
0answers
595 views

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.
0
votes
0answers
25 views

Solving for a subjective prior

Consider an iterative predictive modelling process where, after reviewing diagnostics and predictions, parameters are adjusted/constrained and another iteration of modelling occurs. Also note that the ...
0
votes
1answer
190 views

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 ...
5
votes
1answer
78 views

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 ...
1
vote
0answers
25 views

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 ...
0
votes
1answer
123 views

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 $\...
1
vote
1answer
726 views

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 $\...
2
votes
0answers
109 views

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 ...
3
votes
2answers
612 views

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 ...
0
votes
1answer
165 views

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{\...
1
vote
1answer
207 views

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 ...
2
votes
1answer
442 views

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 ...
1
vote
1answer
232 views

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....
0
votes
1answer
124 views

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 ...
2
votes
0answers
362 views

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 ...
0
votes
0answers
72 views

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?
2
votes
2answers
165 views

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 ...
1
vote
0answers
17 views

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 ...
1
vote
0answers
27 views

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: ...
0
votes
0answers
35 views

$X\sim \mathcal{N}(\theta,\sigma^2)$, $\pi(\theta,\sigma^2)\propto 1/\sigma^2$, $Y\sim \mathcal{N}(\rho X,\sigma^2)$, $\rho$ 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,\...
2
votes
0answers
14 views

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 ...
2
votes
0answers
19 views

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 (...
5
votes
1answer
264 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 ...
2
votes
1answer
86 views

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 ...
2
votes
0answers
30 views

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 ...
0
votes
1answer
51 views

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 ...
2
votes
0answers
42 views

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'...
5
votes
1answer
3k 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 ...
1
vote
0answers
105 views

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 ...
1
vote
1answer
87 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 $B$ ...
1
vote
0answers
27 views

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': ...
1
vote
0answers
26 views

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 ...
0
votes
1answer
512 views

What is the interpretation for the priors in the derivation of Laplace smoothing? [duplicate]

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}(...
1
vote
0answers
17 views

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\...
1
vote
0answers
73 views

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 ...
4
votes
3answers
1k views

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 ...
1
vote
0answers
67 views

Uninformative priors for variance distribution in hierarchical bayesian models

I read that uninformative priors for population variances are often represented by invgamma(eps,eps) where eps could be 1, 0.1 or 0.001. In my model I used these but variance sometimes goes upto ...
1
vote
0answers
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 ...
9
votes
1answer
754 views

Uninformative prior density on normal

Bayesian Data Analysis (p. 64) says, regarding a normal model: a sensible vague prior density for $\mu$ and $\sigma$, assuming prior independence of location and scale parameters, is uniform on $(\...
1
vote
0answers
46 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 ...
2
votes
1answer
83 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 ...
1
vote
1answer
102 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 ...