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.

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Confusion about assumptions in classification problems

I was studying Linear Discriminant Analysis, and this general case came up which used Bayes theorem. Suppose we observed response values of $Y \in \{0,1\}$ and predictors $X \in \mathbb{R}$. Suppose ...
Mescoman's user avatar
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Comparing Bayesian hierarchical models with different sample sizes

I have observation data covering a certain period of time. I follow a block-maxima approach where the data are segmented into equal time intervals .My goal is to first develop a Bayesian Hierarchical ...
Ahmed Bayomi's user avatar
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Bayes estimator of possion distribution with Pareto prior

Consider a random sample of size $n$ following the possion distribution with parameter $\ln \theta$, that is $$ f(x|\theta)=\frac{(\ln\theta)^x}{\theta x!}, x=0,1,2,\cdots $$ and the prior of the ...
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Analogue of landscape conjecture in likelihood theory or Bayes?

The so-called landscape conjecture in machine learning says that in high dimensions, most critical points of the loss surface are saddle points rather than poor local minima. Out of curiosity I was ...
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Posterior Distribution in a Bayesian Multivariate Normal Model

I am currently working on a Bayesian inference problem and would appreciate some help on computing the posterior distribution of a hyperparameter within a specific multivariate normal model. Below, I ...
Dalek's user avatar
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Bayesian change detection (sampling the posterior of a Poisson distribution)

I'm trying to work out how the posterior of a Poisson distribution is derived to enable me to detect changepoints. I'm trying to follow the example here. $Y_i$ (events per year) is modelled using two ...
unearthed56783's user avatar
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Naive Bayes classification for multivalued marginal

x y z C 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 The dataset in the table above consisting of boolean variables x, y and z and a single boolean output variable C. I ...
Sena Yalçın's user avatar
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Given conjugate prior and posterior distributions, what is the PRIOR predictive distribution? [closed]

I am doing an assignment on my statistics class. We had 1 lecture about bayesian parameter estimation, where we were taught about the following formula (and it's discrete form, if $h(\theta)$ was ...
ampersander's user avatar
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+50

Optimal method for estimating geometric mean ratio using Bayesian log transformed data

I'm working on a Bayesian analysis with a categorical variable involving two groups (A vs B). I'm seeking advice on the best method to compute the geometric mean ratio (GMR) together with the highest ...
mat's user avatar
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Solving for b in inverse-gamma distribution [closed]

I am working through an exercise in the book Bayesian Reliability, where I need to estimate the Alpha and Beta parameters of an inverse-gamma distribution with a M= 1500 and SD=2000. The exercise ...
Chris L.'s user avatar
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When to use fixed effects or multi level models in regression?

Suppose you run an experiment where the treatment is Gatorade and the outcome is one-mile runtime. You’ve stratified on variables such as sex, height and weight so they’re well randomized and have no ...
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Is it possible to estimate effects using Bayesian modelling after matching?

I am following [Greifer 2023][1] to estimate the effect size after (genetic) matching, where I am using bootstrapping to estimate the confidence intervals. Since I have a hierarchical setup with ...
guest1927's user avatar
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Estimating transition probabilities and their ranges

I have a system with multiple states (N) that can transition from one state to another at every discrete time increment, or stay in the same one. I want to obtain a good estimate of the transition ...
Valerio D. Ciotti's user avatar
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Posterior Predictive Distibution

How do we actually calculate (what are the operations that need to be done) the posterior predictive given a vector of observations; can we do away with the assumption of independence? Let's say we ...
George Ntoulos's user avatar
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Estimating expected value with respect to posterior

I have a neural network and I need to calculate the following: $$\mathbb{E}_{P(\theta|D)}[f(\theta)]=\frac{\sum_\theta P(D|\theta)P(\theta)f(\theta)}{\sum_\theta P(D|\theta)P(\theta)}$$ Where $f$, ...
Feri's user avatar
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What is the correct implementation of MCMC

I am learning Markov Chain Monte Carlo (MCMC) simulation as of the moment. My background is civil engineering and please excuse my ignorance if some of the questions are quite obvious. I want to learn ...
ian's user avatar
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so the question is about calculating MAP and PPD. I know the formulas for both, but find it confusing, so can someone explain step by step? [closed]

Now suppose that you run each model, and they make the following predictions: p(yt+1 | yt, θ1) = .4 p(yt+1 | yt, θ2) = .75 p(yt+1 | yt, θ3) = .6. What is the maximum a posterior estimate p(yt+1 | yt,...
Hannan Sandhu's user avatar
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Hypothesis test of a random effect in a Bayesian GLMM using the brm package in R [closed]

I want to test some fixed and also the correlation between random effects of a GLMM model I ran with the brms package in R. Getting a Bayes factor for the fixed effects worked: ...
rbeginner's user avatar
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41 views

Interpretation of Statistical Tests and the Importance of Statistical Power [duplicate]

I was planning on running a statistical test for hypothesis testing, but was confused if statistical power is important once a test is run. Looking at this confusion matrix, one would ideally set ...
stillQuestioning's user avatar
2 votes
2 answers
59 views

prior and posterior predictive distributions, Bayes Theory

Consider the binomial sampling model with a Beta prior on $\theta$ and the prior predictive distribution. Let $n$ be the binomial sample size. \begin{align} p(y^{new}) &= \int_{\theta}f(y^{new}|\...
Curtis00168's user avatar
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Understanding of Gamma distribution as precision prior in Bayesian inference for Gaussian

Christopher M. Bishop in his book "Pattern Recognition and Machine Learning" nicely explains where does Student t-distribution $St(x|\mu,\lambda,\upsilon)$ originate into. In Chapter 2, it ...
baronett's user avatar
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1 answer
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How to statistically discover significant process change effectiveness?

I am currently working on a project where I need to assess the effectiveness of changes made in a production process. Our initial success rate was 50%, and after making some alterations, we've ...
Luxspes's user avatar
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Formal Bayes rule for the bandit problem

We have two slot machines, $B_1$ and $B_2$. We've played the first machine $n_1$ times and gotten the rewards $R_1^1, \dots, R_1^{n_1}$ and played the second machine $n_2$ times and gotten the rewards ...
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Post-hoc test for Bayesian ANOVA in R

I set up an ANOVA to test for a 2-way interaction. However, for my hypothesis I would need to test whether the levels A and B of facor 1 are different for each level of factor 2. In a frequentist ...
rbeginner's user avatar
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Statistical Integration of Bayesian and Frequentist Approaches: Weighing Methodology

I'm uncertain about where to post this question. I'm currently working with geotechnical data (soil parameters) and aiming to obtain realistic and safer parameter values. To achieve this goal, I've ...
JCV's user avatar
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Bayesian account for maximum likelihood estimate over infinite parameter space

Suppose I have some samples $x_1, \ldots, x_n$ from $\mathcal{N}(\mu, 1)$ for unknown $\mu$. Then the maximum likelihood estimate for $\mu$ is just $\overline x = \frac1n \sum x_i$. Ideally, we can ...
user400784's user avatar
1 vote
1 answer
17 views

BVAR model: Draws and Burn-In?

This is a very basic question. I am trying to understand how a BVAR model works. One thing I dont get is why we are using a burn-in period and what we are making "draws" from. I simply can ...
Johanna W's user avatar
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1 answer
43 views

How to deal with interaction terms in regression that cannot have a negative product?

Assume we have the following model: $y = \beta_0 + \alpha_1 * x_1 ^{\beta_1} + \alpha_2 * x_2^{\beta_2} + \alpha_3 * x_1^{\beta_1} * x_2^{\beta_2}$ where as we have the following priors for our IV's $\...
richard baws's user avatar
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1 answer
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Identify outliers in testing data based on trained Gaussian mixture model

I use Gaussian mixture model (GMM) to infer probability density of multidimensional data written as: $p(x) = \sum_{j=1}^{K}\pi_j*N(x|\bf \mu_j, \Sigma_j)$, where $K$ is a number of mixtures, $\pi_j$ ...
baronett's user avatar
1 vote
1 answer
33 views

How come the Bayes Theorem formula results in different probabilities that are verifiable using manual counting?

I assume Baye's Theorem is expressed as either: $P(B|A) = \frac{P(A|B)*P(B)}{P(A)}$ or $P(A|B) = \frac{P(A) * P(B|A)}{((P(A) * P(B|A)) + (P(A') * P(B|A'))}$ The tutorial problem was: Assume ten ...
Joachim Rives's user avatar
1 vote
0 answers
21 views

Large samples property of bayes procedures

I was reading through Wasserman's All of Statistics and I came across this property in the Bayesian statistics chapter: I think I don't really get what is supposed to be the intuition behind it, and ...
DeadKarlMarx's user avatar
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Bayesian statistics for 2 directional tests at the same time

We want to run Bayesian statistics on 2 variables on which the H1 hypothesis to be directional for both of the variables at the same time (ex. A>0 and B<0), while the rest of the case to be H0. ...
user400574's user avatar
1 vote
1 answer
68 views

Bayesian analysis of Plausible Values in large-scale education surveys

Surveys like PISA, TIMSS etc. do not report individual achievement scores per observation, but five (sometimes ten) so-called "plausible values", drawn from a constructed probability ...
Thomas's user avatar
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Modeling the evolution of determinants to support of Quebec indepedence [closed]

I'm working on an political science article where we want to study the evolution of what determines the support to Quebec independence from Canada. We have survey data from 1974 to 2023. More ...
Hubert Cadieux's user avatar
4 votes
2 answers
69 views

Classification error when estimating population size of rare phenomena

I need to understand how a particular statistical challenge has been formally recognised or is commonly described in literature, and what the best academic resources are that discuss it. Here's the ...
geotheory's user avatar
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1 vote
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Mixture of two Poisson distributions

I would like to determine the mixing between two Poisson distribution means. I have $N$ observations that are drawn from two Poisson distributions. Each observation is drawn from one of the two ...
P. Egli's user avatar
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1 answer
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In Bayesian Linear Regression, do I need to take multiple samples of the Posterior for prediction?

Given $$\begin {align} \beta&\sim\mathcal N(1.5,1)\\ y&\sim\mathcal N(\beta x,5.5) \end{align} $$I have 10,000 samples from the posterior $\beta_S\sim P(\beta|x)$ Is it enough to get the ...
wd violet's user avatar
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1 vote
0 answers
66 views

Evaluate CDF and outliers of multidimensional Gaussian mixture [closed]

I use Gaussian mixture model (GMM) to infer probability density of multidimensional data written as: $p(x) = \sum_{j=1}^{K}\pi_j*N(x|\bf \mu_j, \Sigma_j)$, where $K$ is a number of mixtures, $\pi_j$ ...
baronett's user avatar
1 vote
0 answers
24 views

Bayesian Predictive Posterior Distribution for Batch Defect Probability

For a research project, I need to assess the probability that a new batch is defective. I want to use a predictive posterior distribution for this purpose, as it incorporates uncertainty. A beta-...
user1245384's user avatar
2 votes
0 answers
54 views

How does Dempster-Shafer Theory of Evidence relate to Deep Learning?

I am reading this article and it has the following phrase - "Dempster-Shafer Theory of Evidence assigns belief masses a set of classes (unlike assigning a probability to a single class)". ...
desert_ranger's user avatar
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BART with non-parametric heteroscedastic noise?

Is there a variant of BART that robustly captures noise that is both heteroscedastic and non-parametric (or has an a-priori unknown parametric form)? For example, a BART that could fit this test data: ...
Luke Gorrie's user avatar
2 votes
1 answer
51 views

Centering Priors on MLEs vs. Using MLEs as Initial Conditions for MCMC [duplicate]

Here: Centering prior distributions on MLE/OLS estimates I ask about centering priors on MLEs in the context of a logistic regression (in my case with only categorical predictors), which I've seen a ...
compbiostats's user avatar
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How to compute a posterior for the parameter of a model?

I have quite the specific question over a model for which I am asked to compute a posterior. Here are all the details : Bayesian model . For clarity purposes, let $X=[x_1^{\top}, \ldots, x_T^{\top}]^{\...
user20920567's user avatar
2 votes
1 answer
99 views

Is it possible to merge credible intervals from different Bayesian prediction models into a single estimate?

The situation Imagine an archaeological site, 10.0m deep. For my study, I construct an "age-profile" for this site, i.e., I produce a model of age as a function of depth. There are various ...
BabuR's user avatar
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1 vote
0 answers
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Bayesian hypothesis testing using posterior samples of estimated parameter

I'm modeling recruitment curves using a Hierarchical Bayesian model. There is a key parameter in my recruitment curve, let's call it $P$. I have two groups (A and B) of participants of respective size ...
chesslad's user avatar
1 vote
1 answer
68 views

Is there a way to relate $\operatorname{Var}(\theta)$ with $\operatorname{Var}(\operatorname{logit}(\theta))$?

I am doing the above exercise in Jim ALbert's "Bayesian Computation with R", Chapter 5. I have made a normal approximation of the paramater $\eta$, which is the logit of $\theta$. I ...
StAKmod's user avatar
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0 votes
1 answer
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Model most likely coordinates of target using Bayesian

I would like to use a bayesian model to determine which position (X, Y) is most likely the best position to score a goal in soccer. For this I have a dataset of a soccer club with all its goals and ...
Quinten's user avatar
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0 answers
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Specifying priors for bivariate model with both a gaussian and binomial distribution in MCMCglmm

I have two response variables, one is gaussian (parental feeding rate of chicks per hour "Rate_h") and one is binomial (proportion of chicks that survive to fledging "propfledged")....
Acones's user avatar
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0 votes
0 answers
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Difficulties with estimation and strange fitted values for BVAR (BVAR R package)

I'm using the BVAR package in R to estimate a Bayesian vector autoregression involving the following monthly variables: US Capacity utilization, US Total Employees, US PCE index, and 5,10,20,30 year ...
Diego De Vivero's user avatar
1 vote
0 answers
13 views

Expected improvement for bayesian linear regression with unknown noise variance

My question is basically if the expected improvement for a bayesian linear regression with unknown noise variance, i.e. we place a prior on the noise variance -> predictive distribution may not be ...
optimalic's user avatar
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