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
1
vote
0answers
49 views

Failing to simulate data for a negative binomial probability distribution [migrated]

I am hoping someone can help me. In a beginners workshop I attended, in the process of fitting a multiple regression model, the instructor initially established a prior predictive check using a ...
0
votes
0answers
8 views

Can you use a prior on the population distribution when using BTYD?

In Counting Your Customers: Who-Are They and What Will They Do Next?, David C. Schmittlein, Donald G. Morrison, Richard Colombo, 1987. which defines the BTYD model, ...
1
vote
0answers
52 views

Is my Stan model correct? The Jeffreys prior for a heteroscedastic mixed-effects model

I am using rstan to derive MCMC samples from a heteroscedastic mixed-effects model with different residual variances $\sigma_j$ for each experimental condition $j$. One assumption is the Jeffreys ...
2
votes
2answers
218 views

Selecting informative priors

I am questioning myself on how to chose the priors for a bayesian analysis in Rstudio. I'm trying to investigate the chances of relapse in a set of patients. These patients are all affected by a ...
0
votes
0answers
16 views

Setting priors for a beta distribution in R-INLA

I'm running a regression in R-INLA, where the response variable is proportion of grid squares suffering deforestation (by year, over a 20-year period). Setting the response for the last 5 years to NA ...
1
vote
1answer
42 views

Bayesian inference with simple models and many data points: impact of priors and the number of data points

The setting. Let us assume I would like to perform Bayesian inference for a low-dimensional model on a large dataset, i.e., there are many more data points than there are parameters to identify. Let ...
2
votes
1answer
175 views

A transformation from uniform random variable to Gaussian mixture

I am attempting to describe a prior_transform for a multivariate Gaussian mixture in order to estimate the evidence integral of that prior convolved with another likelihood distribution. This is ...
0
votes
0answers
29 views

Prior knowledge in context of nullhypothesis testing

I am currently working through the book Doing Bayesian Data Analysis - John Kruschke and have trouble to reason about a text paragraph [Page 315] Suppose that we are not flipping a coin, but we are ...
2
votes
0answers
509 views

Bayesian prior and posterior computation for a truncated normal

I have to deal with data in a Bayesian framework, ultimately devising a Gibbs sampler for inferring all my distributions parameters. Specifically, suppose I observe some univariate data distributed ...
0
votes
1answer
25 views

How can I choose how confident my beta distributed bayesian prior should be?

I am new to Bayesian statistics, and would appreciate help understanding the Prior. I want to combine a small national dataset with a prior from very large international studies, to give a posterior ...
1
vote
1answer
59 views

Is the prior in Bayes formula a probability or it can also represent a probability distribution?

Given the Bayes formula: $$ p(\theta|D) = \dfrac{p(D|\theta)p(\theta)}{p(D)} $$ If there is a distribution (let's say $g$) over the parameter $\theta$, how should one rewrite the Bayes formula? $D$ is ...
19
votes
1answer
5k views

Why LKJcorr is a good prior for correlation matrix?

I´m reading the chapter 13 "Adventures in Covariance" in the (superb) book Statistical Rethinking by Richard McElreath where he presents the following hierarchical model: (...
1
vote
0answers
33 views

Default Priors for Intercept and Standard Deviations in R package brms

The only resource I found explaining the default priors in brms is its manual (newest version, updated 03/14/2021) for function set_prior(). For the intercept, the manual does not specify how the ...
0
votes
0answers
31 views

Reproduce results of bayesglm with stan_glm

As indicated in the title, I am trying to reproduce the results of the bayesglm function with the stan_glm. In principle, the ...
0
votes
1answer
35 views

Prior for covariance matrix?

Given a set of data $\{(x_i\pm e_{x,i},\,y_i\pm e_{y,i})\}_i$ (with uncorrelated uncertainties), I want to model it as a multivariate Gaussian function with an unknown mean $\boldsymbol{\mu} $ and a ...
0
votes
1answer
384 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}(...
0
votes
0answers
30 views

How to implement a default prior in a stan_lmer() model?

I have found Rouder and Morey (2012) suggesting a default prior of cauchy(0,1). I would like to implement this in a linear mixed effects model I’m computing using stan_lmer(). However I have both ...
2
votes
1answer
321 views

Difference between random effect and fixed effect with regularization/prior

Let's say I have a random effect intercept. For example: lme4::lmer(yield ~ 1 + (1|Batch)) How is that different than just ordinary regression using ...
1
vote
0answers
45 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
55 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: ...
1
vote
1answer
240 views

Priors and nested random effects in MCMCglmm?

I am trying to construct a zero inflation Poisson GLMM using MCMCglmm(). I am new to Bayesian Statistics and this function and I am struggling to understand a couple of things. For my data I am ...
0
votes
1answer
226 views

Generating data from the posterior distribution

Let $$p(D \mid \mu,\sigma^2) \sim \mathcal{N}(\mu,\sigma^2)$$ where $D=(x_1\ldots x_n)$ is my data. I imposed a normal prior on the mean as $$\pi(\mu) \sim \mathcal{N}(\mu_0,\sigma_0^2)$$ Using Bayes, ...
3
votes
0answers
44 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 ...
33
votes
3answers
8k views

Do Bayesian priors become irrelevant with large sample size?

When performing Bayesian inference, we operate by maximizing our likelihood function in combination with the priors we have about the parameters. Because the log-likelihood is more convenient, we ...
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
81 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
27 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 ...
7
votes
1answer
6k views

Choosing prior for $\sigma^2$ in the normal (polynomial) regression model $Y_i | \mu, \sigma^2 \sim \mathcal{N}(\mu_i, \sigma^2)$

I have the polynomial regression model $$Y_i | \mu, \sigma^2 \sim \mathcal{N}(\mu_i, \sigma^2), i = 1, \dots, n \ \text{independent}$$ $$\mu_i = \alpha + \beta_1 x_{i1} + \beta_2 x_{i2} + \beta_3 x^2_{...
2
votes
0answers
32 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
14 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 ...
2
votes
0answers
234 views

R- Non-informative vs Informative Prior for Bayesian Logistic Regression

I'm kinda new to Bayesian Statistics and I'd like to try to fit Bayesian Logistic Regression but I don't have prior knowledge about my dataset. So, I guess I have to use non-informative prior for ...
0
votes
0answers
8 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
17 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
28 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
1answer
666 views

How to calculate the confidence interval with weighted data?

I've done some search for similar questions, but they're not the same as what I'm trying to get. Assume that there's a server that handles requests $r$ and returns a set of items $I_{r}$ of random ...
5
votes
1answer
72 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
1answer
52 views

How do I put different priors on different levels of a categorical variable in brms?

This is a just a coding query from a bayesian novice. I have a model of this type: ...
0
votes
0answers
60 views

Bayesian improper prior on product of parameters

I'm interested in two sets of variables coming from bivariate normal distribution. $X_i$'s iid ~ N($\mu_x$,$\sigma^2$) $Y_i$'s iid ~ N($\mu_y$,$\sigma^2$) and Cov(Xi,Yi)=$\sigma_{xy}^2$. Now $\mu_x$= $...
3
votes
0answers
101 views

Supervised document classification with prior distribution on some features

There is a somewhat off-the-beaten-path supervised document classification problem I am trying to tackle. For the sake of simplicity, let's say we are using the bag-of-words approach. Usually, we ...
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) ...
20
votes
3answers
27k views

How to choose prior in Bayesian parameter estimation

I know 3 methods to do parameter estimation, ML, MAP and Bayes approach. And for MAP and Bayes approach, we need to pick priors for parameters, right? Say I have this model $p(x|\alpha,\beta)$, in ...
0
votes
0answers
46 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
51 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
108 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
121 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
0answers
28 views

Should prior distribution reflect stationarity assumptions?

In the paper Dynamic Hierarchical Factor Models they present a four-level dynamic factor model and estimate it using a Gibbs sampler. One interesting feature of the model is that the error terms are ...
9
votes
2answers
467 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 ...

1
2 3 4 5
17