# 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 ...
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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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
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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 ...
1 vote
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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 ...
1 vote
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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 ...
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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 ...
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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] 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 ...
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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 ...
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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 ...
1 vote
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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 $f$, ...
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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 ...
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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,...
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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: ...
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### 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 ...
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}|\...
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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 ...
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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 ...
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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 ...
18 views

### 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 ...
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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 ...
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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 ...
1 vote
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### 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 ...
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### 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 ...
1 vote
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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 ...
1 vote
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### 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 ...
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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 ...
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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")....