# 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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### Posterior Predictive Distibution [closed]

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 ...
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### Independence of processes vs independence of underlying parameters

I am interested in applying the approach in this paper by Laurent and Legrand: A Bayesian Framework for the Ratio of Two Poisson Rates in the Context of Vaccine Efficacy Trials The context of my ...
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### Regarding samples gotten from MCMC

In one article explaining MCMC, I once read the following statement. The idea of sampling methods is the following. Let’s assume first that we have a way (MCMC) to draw samples from a probability ...
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### How can I compare model performance across datasets of varying sizes?

I have a person wearing 2 sensors. I create two models, one using Sensor-1 and other using Sensor-2 data I have multiple people repeating the same experiment with varying numbers. How do I a ...
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### Bayesian stats and multiple tests

Are Bayesian models subject to the same problems as frequentist ones, where we cannot run a bunch of different models due to Type I error? For example, let's say I have a large data frame on airplanes,...
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### Rescaling matrix W in Random Fourier Features

I came across this beautiful idea of Random Fourier Features by Rahimi and Recht while working on optimising my GP model using Predictive Entropy Search. I understand the overall idea of approximating ...
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### Why do we use hypothesis tests instead of just letting people do Bayesian updates?

Why do we need discretize our judgements using hypothesis tests? Why can't we just have people report the data every time a study is done, and the p-values and effect size, and then report how the ...
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### Which model to use for predicting a categorical outcome based on human-annotated labeling?

I have a reddit dataset with thousands of online posts over the economy and inflation. We have used human-annotation on 60% of posts to determine whether users blame the following entities over the ...
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### Bayes Factor A/B Testing

I am just starting to look at Bayesian statistics and so far I am aware that Bayes factor summarizes some form of evidence of an alternative hypothesis against the null one. As far as I know we can ...
1 vote
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### How is R-squared calculated in the "Blavaan" R package and is it appropriate to use/report in bayesian analysis?

I am using the Blavaan R package to fit bayesian path analysis models. The output includes an R-squared value. It has come to my attention that there are problems with using R-squared for bayesian ...
1 vote
288 views

### How can I find the posterior distribution for gammadistributed data and prior?

I'm working on a project where I believe Bayesian statistics should be useful. However, my knowledge about bayesian statistics are very scarce. Suppose I got data following a Gammadistribution with a ...
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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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### Q: what book on Bayesian statistics, preferably with R? [duplicate]

I am frequentist by training and practice, but I'd like to learn more about Bayesian statistics. I know the basics, but I would be at a loss if I had to, for example, replace my normal ANOVA ...
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### Determining overdispersion of count variable in bayesian model (brms)

I am trying to determine whether my response count data are too overdispersed for a (brms) Bayesian poisson model. I constructed a poisson-generated response variable with low and high levels of noise/...
1 vote
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### What are some good resources on Bayesian unconditional power analysis, besides John Uebersax's article?

I refer to the article "Bayesian Unconditional Power Analysis" by John S. Uebersax (2007). I'd like to explore the subject further. I haven't checked yet the references that the Uebersax's ...
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### How to interpret the population parameters of a Bayesian Hierarchical model?

This is almost certainly a fatal misunderstanding of mine / knowledge gap but I am confused as to how to interpret the population parameters of a Bayesian Hierarchical model. This is incredibly ...
272 views

### pymc3: Updating the standard error prior

I am estimating a Bayesian multiple regression using continuous data on both the dependent variable and the regressors. My goal is to iteratively estimate the coefficient distributions as more data ...
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### Comparing top level group effects using a 3-level hierarchical regression

I would like to detect group effects (if any) along with statistical confidences. I have a hierarchical data set structured as follows: Drug Groups ...
1 vote
666 views

### Making sure that the design matrix is positive (semi-) definite

In Bayesian linear regression, how do I make sure that the design matrix produced by a neural network $\Phi$ is positive definite? Computing the covariance matrix on the weight requires inverting --- ...