# Questions tagged [hierarchical-bayesian]

Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions

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### What variant of logistic regression is correct here?

Here is my setup: I have M=200 municipalities who all rank high in corruption For each municipality, I pick a random sample of ...
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### Bayesian multivariate regression with common coefficients

In a hierarchical model I'm working on, I have $K$ different $N\times P$ predictor matrices, each denoted $X_k$ and $K$ length $N$ outcome vectors each denoted $y_k$. Essentially, I have a ...
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### Hierarchical Time Series Model using Means

Based on my research and (limited) understanding, I am finding that hierarchical time series modeling works by summing the nodes below to create a total value at the higher levels. I am trying to use ...
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### How to represented nested model with a varying slope?

I have a study wherein we enrolled about 40 subjects and from each subject we have collected repeated images of burns on subject's body. Approx. 2 burn locations on the body are selected initially and ...
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### Estimate baseline and relative change in multilevel Bayesian regression with logged and then scaled outcome

I'd like to interpret the results of a Bayesian regression with a log as baseline value (intercept-only model) and relative change (full model). To achieve this I log-transformed the outcome and then ...
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### Multilevel, hierarchical, and structural equation (SEM) models

Are all three of these just terms for the same idea or are there some critical differences? If so, how do they differ both in usage and principle?
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### Bayesian regression for the sum of Gaussians

I'm pretty new to Bayesian statistics and I want to use Bayesian regression on a 2D data set (frequency on x-axis and measurement data on the y-axis) to quantify the uncertainties. The model is a ...
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### Showing the Posterior of Distribution of Normal Data with Uniform Prior on mu and log sigma has a t-distribution with (n-1) df

we were told in class that if you have data x_1, x_2, ..., x_n that are iid normal with mean = mu and variance = sigma^2 and then put a uniform prior on mu (from -M1, to M2) and log sigma (from -M2 to ...
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### Abuse of notation : same function name for different distributions

Is this too much of an abuse of notation to use the same letter, e.g. $f$, to designate the joint - $f(x,y)$, marginal - $f(x), f(y)$, and conditional - $f(x|y), f(y|x)$ - probability/cumulative ...
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### Fitting a single model to different datasets that include different variables

Suppose we have two datasets df_1 with variables {A,B,C} and df_2 with variables {A,C,D} (A & C are the only mutual variable in the two datasets). Our aim is to predict A using B & C or C &...
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### How does group mean centering affect the interpretation of coefficients in a hierarchical model?

I've dived deeply into the literature, but still don't understand if it's necessary to group-mean center my predictors if I'm entering them into a hierarchical model. Surely, if they're being entered ...
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### Is it possible to include integral transformation of a variable in Bayesian hierarchical models?

I am tackling a problem, which might be described by the following analogy: Suppose we have N similar cars riding on the road, and their speed depends on several factors: proportion of chemicals in ...
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### Tied Bayesian Mixture of Gaussians

I am bit confused when it comes to modelling a Bayesian Gaussian mixture model that assumes a shared covariance/precision matrix for all Gaussian components. I followed the derivation in Bishop and ...
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### Is there any way to plot conditional effects on their original scale?

I fit an GLMM with brms effect with normalized continuous covariates. How can I plot conditional effect of one of my continuous covariates in its rescaled (original) scale? I am using ...
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### How can we attribute observations to observers in a hierarchical Bayesian model?

I am trying to make a hierarchical Bayesian model of latent variables based on many observations by noisy oracles. I want to leverage the information of which observations are from which oracles, as I ...
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### Variable selection in Bayesian hierarchical models with R-INLA

I'm working with Bayesian hierarchichal regressions fitted with R-INLA. I would like to simplify my model by reducing the number of covariates. According to my understanding, Bayesian variable ...
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### Causal inference and components relationship

I am fairly new to more advanced stats and I am looking for a way to model the influence of features into one another in a group. Imagine we have 3 people: A, B, C; These people take some time to ...
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### Notation in Bayesian hierachical models: what does * indicate [closed]

I am new to Bayesian Statistics and have a question about the notation *. What does it indicate in the context of hierarchical models ? Cheers