Questions tagged [hierarchical-bayesian]

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

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One-step prediction in JAGS of a dynamic model with unknown variance

I have the following problem. I have a linear dynamic model as follows: $$\theta_{0}\sim N(0,10)$$ $$v,w\sim \text{InverseGamma}(0.1,0.1)$$ $$\theta_{t}\sim N(\theta_{t-1},w), \hspace{0.3cm} y_{t}\sim ...
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Interaction term to hierarchical model

Assume we have a response variable of interest Y and a predictor of interest X1, that might be associated with another predictor X2, and we do a linear regression with interactions: Y = B0 + B1X1 + ...
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Conjugate Hyperpriors

I heard it was possible to have a Bayesian model with likelihood, prior and hyperprior that has a posterior of closed form, by choosing a conjugate prior and conjugate hyperprior. But I struggle to ...
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Bayesian hierarchical model inference problem image segmentation

it might be really confusing question. I am working on my thesis and I am stuck at a problem. It's a problem in image segmentation and finding parameters of border lines of continuous region in an ...
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15 views

Using Hierarchical Gaussian Linear Regression to Inference of a Breakpoint Position

Edit: this question is not a duplicate of imposing a perpendicularity constraint in Gaussian linear regression. Here, the question is about hierarchical reference of the breakpoint position. The other ...
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67 views

Modeling with Negative Probabilities?

Background: As I understand the role of probability in Quantum Mechanics, the idea is that no observable event can have negative probability, but that it can make sense for unobserved quantities to ...
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Posterior-understand troubles in Bayesian Normal hierarchical model

I´m studying the Bayesian Data Analysis book, third edition (link at the end), and has a little trouble dealing with some algebra... here is the context (See pages 113-117) $y_{ij}|\theta_{j}\sim N(\...
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A posterior predictive check using R

Question: On page 120, the data from the SAT coaching experiments were checked against the model that assumed identical effects in all eight schools: the expected order statistics of the effect sizes ...
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Predicted treatment effect for causally related conditions

Let's say there are two medical conditions $A$ and $B$ that are causally-related, i.e. that they share a common etiological process $C$. For example, $A$ and $B$ could be related autoimmune conditions ...
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Analyzing a likert-type item data with repeated measures with logistic ordinal regression

I'm analyzing some Likert-type item for my thesis. After a quick research, I figured out, that instead of using a least-squares regression as conventionally, a logit or probit ordinal regression model ...
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How wide to make priors in a linear regression?

I am running a mixed effects linear regression. Based on previous work I have estimates for the coefficients of each of my fixed effects. I assume that I will centre each of the priors on those ...
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MCMC: potential causes of poor mixing within small parameter space

I am currently running into a peculiar issue where after running a Bayesian state-space model, independent MCMC chains all end up within a small parameter space (say within +/-.01 region), but there ...
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How do I implement non-centered parameterization in rstanarm?

I have seen this suggested as a solution to divergent transitions. However, I don't understand how to do it. Would someone be able to explain how to do this for this example model? ...
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How many divergent transitions are too many?

I am running a Bayesian linear mixed effects analysis. Four chains for 3000 iterations. I end up with four divergent transitions. Is this too many or can I proceed? How do I know if it's too many? I'...
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Rescaling random intercept coefficients from hierarchical logistic regression

My logistic regression model includes an overall intercept, multiple categorical variables + and continuous covariates like so: $logit(\mu)$ = $\beta_0$ + $\alpha_{j}$ + $\gamma_k$ + $\beta$$X$ where $...
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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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27 views

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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47 views

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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23 views

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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39 views

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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26 views

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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23 views

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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1answer
48 views

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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33 views

How to do a choice-based conjoint analysis with multiple regression and 3 levels per attribute?

I'm trying to follow these instructions: https://docs.google.com/spreadsheets/d/1Piw0Fk0XCWBJOHhC8NsljvIPywaBmLdNa8QpEV75fHQ/edit#gid=777817907 to do a choice-based conjoint analysis with multiple ...
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62 views

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
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How to calculate the expected value of the product of two random variables in a hierarchical model?

Consider the model: \begin{align} & X \sim p_1()\\ & Y \sim \mathcal{N}(\mu_Y,\sigma_Y)\\ & \mu_Y \sim p_2()\\ & \sigma_Y \sim p_3()\\ \end{align} where $p_1()$, $p_2()$, and $p_3(...
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"Controlling for a variable" - can I predict from a Bayesian model having set a covariate to zero?

Someone once said that anyone who talks about 'controlling for a variable' probably doesn't understand statistics. I'm one of those people, alas. I've been using the R package Hmsc to build a spatial ...
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How do I deal with the dimension problem in hierarchical Bayesian model like $P(q, v, B|x) = p(x|B) p(B|q, v) p(q, v)$?

How do I deal with the dimension problem in hierarchical Bayesian model like this? $$ P(q, v, B|x) = p(x|B) p(B|q, v) p(q, v)$$ The likelihood function has a 1D and 2D component, and the prior is a ...
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113 views

Is my Stan model correct? The Jeffreys prior for a heteroscedastic mixed-effects model

I am using rstan to derive MCMC samples from a heteroscedastic mixed-effects model with different residual variances $\sigma_j$ for each experimental condition $j$. One assumption is the Jeffreys ...
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How to implement this two-stage regression model (nutrition research)

The textbook Modern Epidemiology 3rd edition (pages 435-437) introduces a very interesting hierarchical model for studying the effect of food consumption on disease. The typical model for studying the ...
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21 views

Properties of joint distribution over observed data generated after training a latent variable model

I have a Latent variable model like this White nodes are observed and gray nodes are latent. $\theta = \{\theta_U, \theta_X, \theta_M, \theta_{MY}, \theta_{UY}\}$ are the parameters of this model ...
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How can I assess within-subject reliability of Bayesian models?

I already posted this question in another forum, but didn’t reach a lot of people (with Bayesian expertise). Hopefully, someone in here can help me out: I would like to do a Bayesian analysis on the ...
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1answer
45 views

Stop stan when it reaches convergence (Rhat = 1) [closed]

I'm doing a Bayesian analysis, which involves changing the warmup and iterations (many times per day). I wanted to know if there is a loop to automatically change warmups and interactions and stop the ...
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70 views

Survival analysis for different diseases on same patients

I want to apply survival analysis on UFC-fights. Each fighter represents a "disease" and each knock-out is a "death". Each UFC fight consists of a number of rounds and the number ...
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27 views

Deviance Information Criterion

I am trying two compare two hierarchical Bayesian models using the following output from R: I have understood that the DIC is used to compare Bayesian hierarchical models and that the lowest its value,...
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36 views

Anova vs linear mixed (random) effect model vs Bayesian analysis in R

I am not an expert in statistics nor in R so I apologise beforehand if my description is unclear at any point because of that. I tested several models for the same problem and would like to understand ...
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34 views

Prior for Variance Covariance Matrix [closed]

Why in Bayesian Hierarchical Modelling the prior corresponding to a Variance Covariance Matrix is taken to be Inverse Wishart Distribution not Wishart Distribution?
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139 views

Conditional posterior distribution of coefficient in logistic regression

I would like to derive the conditional distribution of β in a logistic regression where Y follows a Binomial distribution B(n,p) the probability model is given as: logit(p)=X'β +u+v ; u is spatial ...
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57 views

Best approach for (weakly) informative priors and variable-scaling in hierarchical logistic regression?

I am a PhD student using logistic regression to investigate mental health epidemiology. Since participants in my cohort study have a diagnosis or not (coded 1 or 0) - I'm using logistic regression to ...
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72 views

MLE of $\tau^2/(𝜎^2+𝜏^2)$ for multivariate normal distribution

I have a multiple normal distribution problem. $\underline{𝑋}=(𝑋_1, \dots, 𝑋_𝑝)^T$ is a p-dimensional normal random vector following the $𝑁(\theta,\sigma^2𝐼_𝑝)$ distribution, where $I_p$ is the ...
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28 views

Likelihood from DAG

I am reading a paper, where the authors state a different likelihood function, than the one I keep deriving. Therefore, I was wondering where I am making a wrong turn. The model is a hierarchical ...

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