Questions tagged [bayesian]

Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

5,162 questions
8 views

Is this equation true for any joint probability distribution (used in orthogonality principle proof for estimators)?

Given two random variables $x, y$, is it true that $p(x - \hat{x}|y) = p(x|y) - \hat{x}$ where $\hat{x}$ is a known constant I came across this in this kalman filter derivation, Corollary 3.2.1, ...
39 views

Is it possible for the mean posterior distribution to be higher than the prior distribution?

Basically just the question. I would appreciate a lot if there was an example, if such thing happened. Thanks.
21 views

Stan: Ancova with a Poisson distribution

I am trying to code an Ancova with a block effect for count data. Here I will simplify the Ancova to a simple linear regression with a block effect. As I am using count data with low observed values ...
72 views

Interpretation of confidence interval in Bayesian terms

Motivation: I was standing in front of a class to introduce into the concept of confidence interval using the example of differences in means (purely frequentist setting) and I was torturing the ...
9 views

Bayesian experimental design choosing the support of the distribution

I am not an expert on these topics so any help is very much appreciated. I'm not even sure if this question is trivial. If so, please let me know. General Setup: Consider the problem posed in this ...
13 views

Ridge logistic regression and posterior distribution

We know that glm regression with gaussian prior can be assimilated to Bayesian regression. Let say I fit the model with frequentist approach and I have the optimal ridge parameter. If I want the ...
33 views

9 views

How to estimate the intriscs probability error of a string of character

So my problem is as follow : I have a given string of characters, and I would like to quantify the uncertainty linked to the probability of each letter types in the string, based on there observed ...
16 views

Is it rational to select a parameter posterior value because it maximizes utility, even if probability is low?

I did Bayesian parameter estimation and I have now an estimate of the posterior distribution for my model parameters (say I have 2000 samples). Now I would like to make the optimal decision under my ...
18 views

Calculating the posterior distribution of linear predictor

I am currently fitting a linear regression model in a bayesian framework in R with the package ngspatial. To investigate the quality of fit, I would like to calculate the bayes R2, as suggested here ...
24 views

Bayesian chi-squared tests

I have a dataset with two groups of participants. Each participant performed a repeated measures task on which three types of errors could be made. I want to measure the difference in distributions of ...
11 views

How can you deal with volatility of a metrics that depends on the count of events?

I am using Herfindahl Index metrics to measure the degree of concentration of posts by email, device_id, IP and other variables to identify potential fraud events. For example, a high degree of ...
26 views

optimization based interpretation of Bayes' theorem

I read about one equivalent interpretation of bayes' theorem as follows: $P(\mathcal{M}|x) = \frac{P(x|\mathcal{M})\cdot\pi(\mathcal{M})}{\int P(x|\mathcal{M})\cdot\pi(\mathcal{M}) d\mathcal{M}}$ is ...
142 views

How do Bayesians verify their methods using Monte Carlo simulation methods?

Background: I have a PhD in social psychology, where theoretical statistics and math were barely covered in my quantitative coursework. Through undergrad and grad school, I was taught (much like many ...
31 views

relation among loss function / MLE / Bayesian estimation

I have read a lot of stuff on the relation between minimizing a loss function / maximizing the likelihood / choose a centrality measure of the posterior (Bayesian estimation); but I cannot see a clear ...
11 views

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 ...
30 views

Conditional Probability Table in R

I want to perform Bayesian network analysis in R. I have a large network and i am bit confused with defining conditional probability tables! In my network i have a node with in-degree of centrality ...
47 views

Introduction to Variational Bayesian methods?

I am interested in learning about Variational Bayesian methods. I understand the general idea, explained in Wiki, where the aim is to approximate a posterior using a more tractable distribution, in ...
19 views

JAGS: Posterior Predictive Check for a Logistic Regression Model

I want to perform a posterior predictive check on some simple logistic regression models that I fitted in JAGS. I found a function in the R package jagsUI called pp.check (see doc here: (pp.check ...
26 views

help determining ROPE for bayesian multilevel probit model

I am having difficulty determining a justifiable region of practical equivalence (ROPE) for a parameter from a multilevel probit model Below is the posterior distribution for the fixed-effect of ...
20 views

Posterior convergence in expectation vs probability

Let's assume that we are doing approximate Bayesian inference and compute the convergence of our posterior estimate to the true value of the parameter using Wasserstein distance. Why posterior ...
23 views

39 views

Calibrating LASSO prior (how to select the scale hyperparameter)?

I want to use a LASSO prior (Laplace prior) for a location parameter $\mu$ $$\pi(\mu \mid s) = \dfrac{1}{2s}\exp\left(-\frac{\vert \mu \vert}{s}\right).$$ However, I do not know to calibrate this ...
49 views

Simple up/down vote rating but weighted by number of responses

I am trying to analyse the ratings for restaurants from a website. The rating system on the website is pretty simple: people can up-vote or down-vote. The restaurant is then presented to website ...
Problem Say I have the following function $g(x)$, which is proportional to the density function $f_\theta(\theta)$ of random variable $\theta$, i.e. $g(\theta) \propto f(\theta)$, such that  \...