Questions tagged [prior]

In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.

Filter by
Sorted by
Tagged with
0
votes
0answers
25 views

Information of priors? [closed]

In an assigment I am working on, I am asked to rate the information given by different priors from the most uninformative to the most informative. I am not quite sure how to judge this criterion. Can ...
1
vote
0answers
40 views

What are the bayesian prior distributions to use for a binomial model with unknown $n$ and $p$

I a experimenting with a new MCMC software and before I delve into more complicated models I wanted to run some simple simulations. This is a very very simple simulation, so not meant to be very ...
0
votes
0answers
46 views

bayesian question: why prior = mu * sigma?

I'm doing a course of Fundamental of Bayesian Analysis in Datacamp and these codes were presented. What is the rationale of prior being mu * sigma ? code: ...
3
votes
0answers
42 views

Metrics for assessing the quality of prior distributions

Clarification: My purpose is to compare different methods for selecting/creating priors (or perhaps I should refer to them as predictive distributions for a quantity of interest/parameter). I do not ...
0
votes
0answers
18 views

What are Large Scale and Complicated Priors?

We use priors in Bayesian networks to include prior knowledge in our models. In this context, what are these two terms: -complicated prior -large scale prior I have seen priors like Laplace, zero-mean ...
1
vote
0answers
17 views

How to get prior distribution based on confidence interval [closed]

If we have mean value and 95% confidence interval of a parameter. For example, sensitivity = 0.5, CI = [0.2,0.78](as you can see, it is asymmetric) How to decide the prior distribution? How to ...
4
votes
0answers
78 views

Decision Theory: Why is it called a “least favorable prior”?

I'm currently reading the chapter on Statistical Decision Theory in Larry Wasserman's "All of Statistics". Reading the section 13.4 about Minimax Rules he introduces the so called Least ...
1
vote
0answers
24 views

Postetior from Jeffrey prior of Normal distribtion

Context I am given a sample from normal distribution $v_i \sim N(\gamma \cdot u_i, \sigma^2)$, $i =1,..., n$. I need to obtain the posterior distribution using Jeffreys prior for $\gamma$. My solution ...
2
votes
0answers
28 views

When does this prior dominate likelihood?

This is a simple Bayesian inference problem, where we are trying to infer some weight parameter $w$. Our posterior distribution is $$ P\propto \exp\left(-\frac{1}{\sigma^2} w^Tw\right) \exp\left(-f(w)\...
0
votes
1answer
12 views

Distributions with negative support in JAGS

I am creating a Bayesian regression model where I want to include a prior for a variable that can only have a negative coefficient. What distribution can I use that only has a negative support and is ...
1
vote
0answers
11 views

Prior/Posterior of the Proxy

I am trying to understand a sentence from Caldara and Herbst (2019), who develop a baysian proxy SVAR model. The paragraph is: "In case of weak identification, the prior plays an important role ...
-1
votes
1answer
72 views

How are these priors generated? [closed]

I am trying going through an exercise, I don't understand how the information provided in the text below transitions into the parameters displayed in the beta priors. How are these informative priors ...
0
votes
0answers
7 views

How to create a distribution for a feature that is conditional on more than one other variable

I have a variable, r. It has a distribution P(r). I have found two other variables, A and B that are correlated with r. I want to build a distribution P(r) that is conditional on these two variables. ...
1
vote
0answers
16 views

Prior probability of Normal distribution [closed]

I was solving one problem and got to the point where I needed to find the prior probability of the normally distributed variable, with the known mean and variance. I'm a little confused because I've ...
1
vote
0answers
22 views

Prior for Variance Covariance Matrix [closed]

Why in Bayesian Hierarchical Modelling the prior corresponding to a Variance Covariance Matrix is taken to be Inverse Wishart Distribution not Wishart Distribution?
0
votes
0answers
15 views

Bayesian Multinomial in rating

I have a dataset that has two columns:2)The rating of a product from 0:5 and 2) the numbers of votes.Can i make a Bayesian analysis with rating following a multinomial distribution (categories 1-5) ...
0
votes
0answers
44 views

What is the posterior distribution $p(\textbf{f} | \textbf{y})$ for a Gaussian Process regression?

What is the posterior distribution $p(\textbf{f} | \textbf{y})$ for a Gaussian Process regression? Suppose that $p(y_n |x_n, f) = N(f(x_n), \sigma^2)$ with prior on $\textbf{f} = [f(x_1), \ldots f(x_n)...
0
votes
1answer
45 views

Prior distribution on Bayesian T Test?

I have two subgroups of structure (bone structure) and I want to test if there is any difference of size (area) between them, and if there is, how important this difference is. The first set is a ...
4
votes
2answers
96 views

What is Cromwell's rule and why is it important for Bayesians?

I have just heard of Cromwell's rule, but I'm not sure I understand it very well. What is Cromwell's rule and why is it important for Bayesian statistics?
3
votes
1answer
119 views

Showing $X\sim \operatorname{Poi}(\lambda)$ is minimax

Assume that $X$ has $\operatorname{Poisson} (\lambda)$ distribution and the loss function is $\ell(\lambda,a)=\frac{(\lambda-a)^2}{\lambda}$. Now, I want to show that $X$ is minimax. A hint that is ...
1
vote
1answer
23 views

How should past experiments inform power analysis?

One crucial step in power analysis is to guess the effect size. Luckily, I do have 1 similar past experiment. So I do have 1 data point instead of completely guessing what the effect size is. However, ...
0
votes
0answers
20 views

Converting posteriors to likelihoods by removing prior

I have a set of MCMC chains (i.e., unnormalized posteriors) for a parameter I modeled for a sample of objects. I have a model that requires that I condition on the likelihoods of this parameter. My ...
9
votes
2answers
380 views

What is the “effective sample size” of the prior in Bayesian statistics?

In Bayesian statistic, what is the mathematical definition of "effective sample size" of the prior? Could you provide what the "effective sample size" is for the well known classes ...
0
votes
1answer
78 views

Maximum a posteriori estimate with exponential prior

Lets say that I have N observations that are poisson and i.i.d. The prior is an exponential with parameter 2. I know that the exponential distribution is given by $ \lambda e^{(-\lambda x)} $ But how ...
0
votes
0answers
81 views

Mathematical foundations to justify the “existence” and appropriateness of using prior distributions?

I claim that there is no a priori reason I should use a probability distribution to express uncertainty about models, claims or parameters. Apparently, (some) Bayesians disagree with that, as they ...
0
votes
0answers
16 views

Should you multiply every observation with the prior when calculating the maximum a posterior?

Lets say I have a number of observations and a prior. The observations are poisson distributed, are i.i.d and the prior is exponential with paramater 2. I want to calculate the maximum a posterior ...
0
votes
0answers
11 views

How do I get around this “Argument 'coef' may not be specified when using boundaries.”

I have a model, the brms code is given below. It is a system of equations (I am estimating demand for two categories of goods). Economic theory tells me that the intercepts have to be restricted to ...
0
votes
0answers
7 views

Understanding of scale loss with Gaussian prior

I am reading a paper called PHOSA wherein a scale loss is used. I had the following questions regarding this scale loss in equation 8: What part of this loss function is actually incorporating a ...
1
vote
0answers
48 views

Determining the Likelihood function from a Uniform Prior

I am trying to find the Bayes factor between two models, which I understand is the ratio of the likelihood functions of each model. The second model has a uniform prior described by: $U(A; -a, a) = \...
0
votes
1answer
36 views

How is the likelihood different from the posterior? [duplicate]

I come from an applied mathematics background and have never looked at statistics, but I started studying Machine Learning recently. One thing that I am struggling to understand is: what is the ...
0
votes
0answers
19 views

Determining the mean of a posterior probability

There is a comet whose model show it is moving along a straight line $$ x(t) = mt + b $$ The posterior predictive distribution of a comet's position, which is $$ PPD(x) = p(x|t,d) ∝ \exp\left( -\frac{...
1
vote
1answer
74 views

Confusion about prior used in Recursive Bayes Filter

I'm currently using this thesis to understand key concepts about probabilistic inference in computer vision which is being a great source. The frame of the question is the following: Let us assume we ...
0
votes
0answers
152 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.
2
votes
1answer
43 views

How to calculate the posterior distribution from the density

I'm stuck on a answer from an old exam. The task is to use a Poisson distribution and a Gamma distribution as prior to calculate the posterior density: $$ p(\lambda|x) \propto L(\lambda)p(\lambda)\...
4
votes
1answer
24 views

How to jointly model $N$ groups where data in each group is i.i.d. Normal and infer the posterior distribution?

I am given the following data of income scores of individuals from $N$ groups: $$(\textbf{x}_1, \textbf{x}_2 \ldots \textbf{x}_N),$$ where $$\textbf{x}_j = (x_j^1, x_j^2 \ldots x_j^{N_j}),\quad j = 1, ...
2
votes
0answers
27 views

Choosing the Dirichlet prior in a mixture model

Consider the following mixture model with $K < \infty$ components, $$ f\left(x \mid \theta_{1}, \ldots, \theta_{K}, \pi_{1}, \ldots, \pi_{K}\right)=\sum_{k=1}^K \pi_{k} \varphi\left(x \mid \theta_{...
0
votes
0answers
19 views

What is the “prior standard deviation of the modelled predictive means” and how do you calculate this?

In the book Regression and Other Stories (Gelman et al., 2021, p. 208), there is an example where a multi-linear regression model has: $26$ coefficients; standardised predictors with mean $0$ and ...
1
vote
2answers
80 views

Bayesian Statistics: Properly updating the Prior for new analysis

I have three tables of information about $A$ and $B$ (gray cells, black font), their row and column marginal totals (black cells white font), and the grand total (white cell black font). The first two ...
0
votes
1answer
23 views

How to choose priors for experimental data

My question results from the subjectivity of priors, and if there are bodies of work that help to create a more objective approach towards prior choices. My question specifically is to do in the realm ...
1
vote
1answer
62 views

Expression for the prior predictive density for a multivariate normal distribution with unknown mean and unknown variance?

I am trying to find the expression for the prior predictive density for a multivariate normal distribution with unknown mean and unknown variance. In the short document Bayesian Inference for the ...
4
votes
1answer
55 views

Does incorporation of prior expert opinions with Bayesian analysis actually work in practise or is it too much to ask of non-statisticians?

Suppose we have a sample from some population of people and we want to perform Bayesian regression of height vs weight using this sample. Suppose the true relationship between height $y$ and weight $x$...
0
votes
0answers
15 views

Hierarchical clustering with a prior

I would like to perform a clustering (in the best case scenario a hierarchical clustering) of N entities and the distance among those entities is a known input. I also have an a priori on the ...
1
vote
0answers
47 views

Noninformative prior distribution: uniform or normal? [closed]

The uniform distribution, with the support that has a finite measure, guarantees that the entropy is maximum(as stated in this answer), but in our daily life, normal distribution seems more ...
0
votes
0answers
18 views

Can a range of priors being used for a linear regression be applied to a logistic regression?

I have trial level data from a study in which participants responded to a series of stimuli. I have a predictor of interest. For the sake of this example, let's call it the size of the stimulus. There ...
2
votes
1answer
62 views

Theoretical Justification for Zellner's g Prior

What is the theoretical justification for Zellner's g prior for linear regression? I cannot see how it is possible to justify from a purely Bayesian perspective, in which probabilities are epistemic, ...
0
votes
0answers
49 views

Prior and posterior distributions involving a prior Beta distribution [duplicate]

Question: A poll is conducted to help ascertain whether the Labour party candidate or Tory candidate will win in a forthcoming election for Coventry Mayor ( there are no other candidates, and the ...
0
votes
0answers
52 views

What does it mean to say that “the prior over $f$ induces a prior over probabilistic classifications $\pi$”?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: We now turn to the ...
2
votes
1answer
69 views

Gaussian processes: The uncertainty is reduced close to the observations?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: In this section we ...
8
votes
3answers
309 views

Why does a function being smoother make it more likely?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: Given this training ...
5
votes
1answer
67 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
2 3 4 5
17