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
1 vote
0 answers
22 views

Noninformative prior for Gaussian precision as the special case of Gamma distribution with both parameters being zero

The question is from page 120 of book "Pattern Recognition and Machine Learning" by Christopher M. Bishop. I excerpt it as follows: The definition of gamma distribution $\textrm{Gam}(\...
user avatar
  • 45
0 votes
1 answer
58 views

Is there any strong argument about objective/non-informative improper prior?

Decades ago improper objective priors - e.g. $\pi(\sigma) \propto \sigma^{-1}, \sigma > 0,$ for a scale parameter - were considered problematic because some authors thought they were leading to the ...
user avatar
  • 41
0 votes
0 answers
24 views

Non-informative prior of a geometric distribution [duplicate]

If we are given a standard geometric distribution $(1-p)^{x-1} p$, with $0<p<1$ what would be a suitable non-informative prior for this?
user avatar
1 vote
2 answers
154 views

Informative priors for standard deviation (or variance)

Suppose I want to perform Bayesian estimation of the mean $\mu$ and standard deviation $\sigma$ of a Gaussian distribution. Is there a standard way to specify an informative prior over $\sigma$, ...
user avatar
12 votes
2 answers
654 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 ...
user avatar
  • 1,726
0 votes
0 answers
10 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 ...
user avatar
0 votes
0 answers
16 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(\...
user avatar
  • 101
1 vote
0 answers
80 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 ...
user avatar
4 votes
4 answers
160 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 ...
user avatar
  • 6,014
0 votes
0 answers
19 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 ...
user avatar
4 votes
1 answer
174 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 ...
user avatar
  • 163
2 votes
1 answer
82 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 ...
user avatar
  • 479
1 vote
0 answers
1k 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.
user avatar
1 vote
1 answer
356 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 ...
user avatar
  • 5,376
5 votes
1 answer
89 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 ...
user avatar
  • 341
1 vote
0 answers
27 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 ...
user avatar
  • 772
0 votes
1 answer
165 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 $\...
user avatar
1 vote
1 answer
1k 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 $\...
user avatar
2 votes
0 answers
142 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 ...
user avatar
3 votes
2 answers
878 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 ...
user avatar
  • 595
0 votes
1 answer
173 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{\...
user avatar
  • 595
1 vote
1 answer
293 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 ...
user avatar
  • 191
2 votes
1 answer
817 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 ...
user avatar
1 vote
1 answer
336 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....
user avatar
0 votes
1 answer
129 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 ...
user avatar
  • 47
2 votes
0 answers
515 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 ...
user avatar
  • 197
0 votes
0 answers
95 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?
user avatar
  • 327
3 votes
2 answers
189 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 ...
user avatar
1 vote
0 answers
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 ...
user avatar
1 vote
0 answers
38 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: ...
user avatar
0 votes
0 answers
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,\...
user avatar
  • 1
2 votes
0 answers
17 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 ...
user avatar
  • 1,561
2 votes
0 answers
21 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 (...
user avatar
5 votes
1 answer
334 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 ...
user avatar
  • 1,254
2 votes
1 answer
113 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 ...
user avatar
2 votes
0 answers
31 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 ...
user avatar
0 votes
1 answer
59 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 ...
user avatar
2 votes
0 answers
46 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'...
user avatar
5 votes
1 answer
5k 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 ...
user avatar
1 vote
0 answers
116 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 ...
user avatar
1 vote
1 answer
88 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 $B$ ...
user avatar
1 vote
0 answers
28 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': ...
user avatar
  • 51
1 vote
0 answers
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 ...
user avatar
0 votes
1 answer
689 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}(...
user avatar
  • 101
1 vote
0 answers
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\...
user avatar
1 vote
0 answers
83 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 ...
user avatar
  • 913
4 votes
3 answers
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 ...
user avatar
  • 1,630
1 vote
0 answers
79 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 ...
user avatar
1 vote
0 answers
23 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 ...
user avatar
9 votes
1 answer
864 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 $(\...
user avatar
  • 1,459