# 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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### How to analyse data with both GLMM and bayesian GAMM

For my master's dissertation, I am working in R with a dataframe that is: repeated measures, negative binomial and zero-inflated. Variables have been factorised (if categorical), centered (if ...
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### Is the conditional probability fallacy exising in the case of an individual with full control [closed]

Hello I had a very interesting discussion and I need your help in clarifying the correct answer. TLDR: Problem statement for a layman: Given I am a woman and I want to become professor, and given that ...
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### How to test whether null effect of condition is due to ceiling effect?

I have data from an intervention study on math learning. Participants were assigned to four treatment conditions in a 2*2 between-participants design. Participants were tested before the intervention (...
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### How to Compute Mean Ratios and Their 95% Confidence Intervals in a Bayesian Model

I am working on a Bayesian model using the brm function from the brms package in R, and I am interested in comparing mean responses of different groups. Specifically, I would like to calculate the ...
1 vote
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### Bayesian hierarchical exchangeability assumptions reasonable with a check treatment?

This is information I believe to be true A practical feature of hierarchical Bayesian models is that partial pooling reduces (eliminates?) the need of adjusting for multiple comparisons when ...
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### MCMCglmm package [closed]

the summary() for my ordinal model isn't returning all of my cutpoints. There are four levels in my response variable but I'm only getting two cut points. Does anyone know why?
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### where's a good reference and community for help with getting started on Bayesian time series analysis?

I am trying to learn the basics of Bayesian time series analysis, but am having trouble finding some up-to-date basic examples and a discussion forum where I might be able to get some guidance. (...
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### Prior probability distribution when we have a single estimate of the mean and no estimate of the variance

Say we have some real parameter $p$ we'd like to determine experimentally. If we have a single estimate of $p$ but no associated uncertainty, what prior probability distribution(s) can/should we use ...
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### Bayesian data analysis numerical [closed]

How do I solve the following problem? Suppose that $x_1,x_2,...,x_n \sim U(0,θ)$ i.i.d. given $θ$ and suppose that $θ$ has the prior pdf: $$p(θ) = (a/θ_0) * (θ_0/θ)^{a+1} I[θ > θ_0], a > 1$$ a) ...
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### Is bayesian updating framework a valid concept?

When I google search for the term, only 6 pages showed up. There is no authoritative paper on this, except https://arxiv.org/abs/1306.6430 which argues for using informatics concepts to generalize a ...
1 vote
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### Why do T prior and likelihood make a bimodal posterior?

In this post, the author shows that when a likelihood and prior are both T-distributed with $2$ degrees of freedom, the posterior is bimodal. The given reason is that The two modes persist - the ...
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### How can I restrict the predicted values of a bayesian linear regression?

Is there a way to restrict the predicted values, say, to only positive values or an interval of values? Let's say I want to estimate a linear model, y = a + Xb, using Bayesian techniques. I specify ...
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### Please help me evaluate these results if a Bayesian Mixture Model is better than K-Means Clustering

Dataset I am performing Clustering in this dataset which some samples are: Now, I am comparing the results of: K-Means Clustering Bayesian Mixture Model (BMM) I set $K=6$ clusters for both of them ...
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### Do we need stationarity for Bayesian network modelling?

Most of the Bayesian network packages in R dealing with continuous data require data to be Gaussian. Does this necessitate the data should also be stationary in order to run the model?
1 vote
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### Two different methods to plot residuals with rstan but two different distributions [closed]

The following is the first exercice of chapter 5 from the Book 'Bayesian Statistical Modeling with Stan, R and Python' of Kentaro Matsuura, 2023. I am fitting a bayesian linear model in rstan and I ...
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### Using mcmc to estimate parameters of Dirichlet distribution

We have a probabilistic model with two parameters, $\theta$ and $\eta$, both of which are uniformly distributed between 0 and 1. The model has five possible outcomes, and the probability of each ...
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### Calculate acceptance ratio of Jacobian of split-merge RJMCMC

I am keep studying the RJMCMC and want to ask question regarding the acceptance ratio of split/merge step of RJMCMC The split/merge step, suggested by Richardson and Green (1997) is following for w_j, ...
1 vote
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### How to obtain marginal density [x], given [y|x] and [y]

I came across a problem knowing density of Y, conditional density of Y given X, how would I obtain density of X? Or would this even unique?
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### Scoring races + ranking index, with Bayesian approach

Challenge: Is this the best approach for scoring multicompetitor races? How do I account for both uncertain prior & uncertain evidence when scoring? Case: athletes getting scores in each race, ...
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### What is Bayesian PCA and its cousin?

When I think of the phrase "Bayesian PCA" I think of two things, but these two things are what I have contrived rather than conventional notions. I would appreciate guidance on what these ...
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### How to take a negative ranged prior using pymc package?

I was trying to fit bayesian linear regression using pymc package. But for certain model coefficients I need to choose the prior as a negative ranged distribution (for example negative halfnormal) so ...
1 vote
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### Do Bernardo Priors still Encounter Paradoxes?

I heard that Bernardo Priors are better versions of Jeffrey's prior that work in multi-dimensions & match frequentist confidence intervals. Apparently they also dodge many paradoxes of other ...
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### For mixed effects model with multiple random intercepts, are bayesian approaches (with MCMC) more robust than frequentist?

I stumbled upon this particular webpage from UCLA containing the following text: [...] Inference from GLMMs is complicated. Except for cases where there are many observations at each level (...
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### Definition of priors for GLM

I am building a generalized linear model using the logit function in R using JAGS. Whenever I saw code people only define priors for the parameters of the model, but never for parameters of the ... 185 views

### Terms and assumptions in trans-dimensional MCMC (RJ-MCMC) for Green 1995 paper

I want to use Trans-dimensional MCMC in my research and for fundamental understanding, I am trying to learn from Green (1995) paper, which is foundation of RJ-MCMC. In part of 3.3 'switching between ...
1 vote
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### In the Monty Hall problem, does it matter that the host knows which door the car is behind? If so, why?

If I'm thinking about this correctly, regardless of how the host chooses which door to open, there's a 1/3 chance the player initially picks the door with the car behind it, in which case they shouldn'...
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I am considering a Bayesian linear model for which the prior is not proper. The model is as usual $y = X \theta + w$ where $w \sim N(0, \sigma^2)$, and $\theta, \sigma^2$ are unknown. The distribution ...