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Questions tagged [hierarchical-bayesian]

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

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0answers
23 views

Finding the mode of the posterior distribution

I have the following hierachical bayesian model - $\mathbf{x}|\mathbf{c},\sigma^2 \sim \mathcal{N}(\mathbf{x}|\mathbf{c},\sigma^2)$ $\mathbf{c}|\mathbf{c}_1,\sigma^2_2 \sim \mathcal{N}(\mathbf{c}|\...
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1answer
48 views

How to choose the best method to generate random values [on hold]

In my specific case, I have a pdf that has no closed form, and I want to generate random values ​​of this distribution. It depends on a summation that goes to infinity (coming from a poisson process) ...
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0answers
19 views

How to fit a hierarchical linear mixed model in Stan? [closed]

I'm trying to fit a linear mixed model of the following form to some data on a particular gene, $g$: $$ y_{d,l,c,t,s}^g = \mu_g + \beta_d + \beta_{d,l} + \beta_{d,l,c} + \beta_{d,l,c,t} + \beta_{d,l,...
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19 views

Complete a Bayesian Network by specifying the probability distributions

I have a hierarchical Bayesian Network like this: Here: $R≡$ log level of poisonous gas (radon) in a house $B≡$ type of house (With a basement or without) $C≡$ a county in Minnesota where the ...
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2answers
45 views

Formal Bayesian justification of conditional modelling

I'm having some trouble following the logic of this passage from Chapter 14 in Bayesian Data Analysis, A. Gelman: The numerical 'data' in a regression problem includes both $X$ and $y$. Thus, a ...
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0answers
18 views

Covariance matrix for multilevel data [closed]

I have multilevel data and I want to compute corresponding covariance matrix. Are there any methods or theory how can I do that?
2
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1answer
29 views

How do Bayesian hierarchical models adaptively learn the prior?

It seems the main difference between a hierarchical and a non hierarchical model is that the hierarchical model learns the prior. That is it adaptively comes up with a regularizing prior to be applied ...
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0answers
29 views

Bayesian estimation in 2x2 mixed design study

I'm trying to correctly set up Bayesian parameter estimation for a mixed-design study with one 2-level between-groups independent variable and one 2-level within-subjects independent variable. The ...
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0answers
11 views

Can Deviance Information Criterion be used for model comparison when the response variable has Poisson distribution?

I just constructed a Bayesian Hierarchical Model for my response variable Y that follows Poisson distribution with the parameter $\lambda$. In my model, I have modelled $log(\lambda)$ as a linear ...
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0answers
27 views

How to evaluate double Integral with importance sampling

I am trying to recreate the Bayesian Hierarchical Clustering algorithm using Python. The example in section two requires evaluating the following double integral (univariate case): \begin{align} p(...
0
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1answer
28 views

Am I doing hierarchical bayesian regression?

I'm doing a Bayesian logistic regression to predict the probability of my dependent variable Y with two predictors, one continuous (X) and the other categorical (C). I deal with C by building 3 models ...
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0answers
16 views

Marginal Distribution of Hierarchal Model Normal distribution with unknown mean and precision

I am trying to use a Hierarchical model where there I have a normal distribution with random mean and precision: $$ y \sim N(\mu, \tau)\\ \mu \sim N(M, T)\\ \tau \sim Gamma(\alpha, \beta) $$ I'm ...
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0answers
15 views

In a Hierarchical Bayesian Model, how can we sample and see how a prior distribution looks like if it contains hyperparameters with hyperpriors?

I have a Bayesian Hierarchical Model that looks like: \begin{equation} Y_i \sim N(\mu, \sigma^2) \\ \mu \sim N(\mu_0, \sigma_0^2) \\ \sigma^2 \sim Gamma(1,1) \\ \mu_0 \sim N(0,1) \\ \sigma_0^2 \sim ...
2
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1answer
36 views

Out-of-sample predictions for mixed model are the same as naive model (ignoring the random effects)

I have a dataset that consists of subjects coming into the clinic (for treatment of another disease) and they are screened for Tuberclosis (as they are a high risk population). Every time they are ...
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0answers
19 views

In a Multi-level Bayesian Hierarchical Model, would higher level parameters be affected by how they are jointly modeled in lower levels?

Suppose we have a Multi-level Hierarchical Model where: $$ \begin{equation} Y_{0i} \sim Bin(\theta_{0i}, n_{0i}) \\ Y_{1i} \sim Bin(\theta_{1i}, n_{1i}) \\ \theta_{0i} \sim Unif(0,1) \\ log\left(\...
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1answer
52 views

Is the methodology for my undergrad dissertation sufficient - should I use a hierarchical negative binomial model instead, despite beginner ability?

As said in the title, I know almost nothing about statistics. My hypothesis for my dissertation is that UK Members of Parliament with a larger margin of victory will do less work than those with a ...
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0answers
20 views

Bayesian concepts : multivariate mixed models

I am working with a multilevel multivariate mixed mode with 4 outcomes. I am having difficulties extracting the variances, coefficients of variations. Could anyone advise? I am new to bayesian ...
1
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1answer
66 views

computing the distribution over the latent function values with the form of a GP predictive

If we have a latent state space $\mathbf{X}$ and the observations $\mathbf{Y}$ and the transition function between two states $\mathbf{x}_{t-1}$ and $\mathbf{x}_{t}$ is given by $\mathbf{f}$ which is ...
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0answers
13 views

A node in Bayesian network model with a hybrid parents (i.e., contentious and discrete Parents)

I have a Bayesian network model that has a node with hybrid parents. Assume that the discrete nodes are beta distributed and the continuous is CLG (continuous linear Gaussian) distributed. If I ...
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0answers
14 views

Bayesian Hierarchical Clustering: How to calculate probability of Data under $H_1$?

I am working on implementing the Bayesian hierarchical clustering algorithm found here from scratch as a way to practice and learn the algorithm. However, I have hit a snag in calculating the quantity ...
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0answers
15 views

Which gradient to compute in a hierarchical model for M-H MCMC?

We have the following model: $$y_t=Mx_t+\epsilon_t$$ with $M$ being a matrix such that $M\sim F_{\lambda}$(assume it's a conjugate prior). The $\lambda$ does not appear in $M$, only in its ...
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0answers
25 views

Hierarchical Choice based Conjoint analysis on transaction data

I want to get the utility of each level of each attribute for every transaction(at a customer level). How can I do that in python/R(could find a good way to do this in python so I tried using ...
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0answers
11 views

Multilevel modeling, constraint for positive values

I'm currently trying to fit a shifted inverse gaussian to reaction time data (always postive). My paramterization of the model includes 3 parameters, alpha, gamma and tau, which must always be ...
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0answers
25 views

Finding mode of posterior using Newton method in R

I am attempting to approximate the posterior $\tilde{\pi_{G}}(z|\theta,Y)$ which is the Gaussian approximation to the full conditional of $z$, and in order to do this I need to find the mode $z^{*} \...
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0answers
15 views

Posterior predictive check for capture-recapture data using jagsUI wrapper

The R package jagsUI is a wrapper for JAGS that has some awesome functions, including a posterior predictive check. As discussed here, you simulate the new data for the parameters based on the ...
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0answers
57 views

Posterior predictive distributions and predictive intervals

I'm confused about the role of posterior predictive distributions in Bayesian inference and predictive inference. As I understand it, the frequentist approach would typically involve fitting the MLE,...
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0answers
40 views

Hierarchical bayesian model: should I account for lack independence?

I am working with vegetation surveys that were conducted in several river networks. See the attached image that shows one of the those river basins/networks. I am interested in analyzing how the ...
4
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2answers
307 views

Differences between prior distribution and prior predictive distribution?

While studying Bayesian statistics, somehow I am facing a problem to understand the differences between prior distribution and prior predictive distribution. Prior distribution is sort of fine to ...
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0answers
29 views

Metropolis-Hastings Algorithm for Bayesian Hierarchical model

I have developed a Metropolis-Hastings Algorithm for a double sigmoidal model, but now the aim is to create a Bayesian Hierarchical model that depends on incoming temperature data. For example, the ...
1
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1answer
54 views

Generalization performance in Bayesian errors-in-covariates model

I'm working on a model with this basic structure: The square nodes are data, and the round nodes are parameters and/or latent variables. The left plate represents the "training observations" we ...
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0answers
34 views

Displaying three-level multilevel model in vector notation

I estimated a three-level multilevel model in stan but I have some trouble writing it correctly in terms of vectors and matrices. Now, I have the following: $\begin{equation} \begin{gathered} y_{ijt} ...
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0answers
35 views

Interpreting Hierarchical Bayesian Model, how to do paired t-test?

I have two hierarchical models. Both models include 80 participants and output both a group-level posterior distribution and 80 individual-level posterior distributions for my variable of interest. ...
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0answers
70 views

A hierarchical Bayesian model in pymc3

Suppose we have the following model: $X$ unobserved $Y$ such that $Y|X \sim \mathcal{N}(X,\sigma^2)$, observed $Z$ such that $Z|X \sim \mathcal{B}(1,X)$, observed and suppose, given observed data $...
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0answers
36 views

Hierarchical time series using DLM

I am developing a forecasting solution using R's dlm package and it is proving to be very useful for most of our requirements. However, I am also keen on sharing information among different time ...
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0answers
16 views

Spatio-tempral Bayesian Poisson model convergence investigation

I am fitting a spatio-temporal Bayesian Poisson model with 22 explanatory variables, an offset variable, 2200 observations and non-informative priors. I am using the package ...
0
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1answer
68 views

bayesian predictions in multilevel model for panel data

I want to make predictions for a bayesian multilevel which basically looks like: $y_{it} = \alpha_{i} + x_{it}\beta$. I was told that I could make predictions by using (in the case that $y_{it}$ is ...
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0answers
17 views

Bayesian hierarchical temporal models

I have been asked recently to transform an already existing Bayesian hierarchical model into an non-stationary model by making the input and the latent variable time dependent(or non stationary). let ...
0
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1answer
77 views

Hierarchical Bayesian Negative Binomial model with Gamma prior on mean

I am interested in deriving the full conditional for the mean parameter in a Neg-Binomial model with a Gamma prior on the mean, as such: \begin{align*} Y|\lambda,\phi\sim & NB(\lambda,\phi)\\ \...
0
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0answers
40 views

Random effects vs Rubin's rule to obtain pooled parameter estimates from multiply imputed datasets

I would appreciate any help to understand the statistical difference between using random effects and Rubin's rule to obtain pooled parameter estimates from multiply imputed datasets. For example, if ...
0
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0answers
38 views

Bayesian analysis of multilevel model with lagged dependent variable

Currently, I am constructed a bayesian multilevel model to analyze a panel data set which now basically looks like the following: $y_{ijt} = \beta_{0ij} + X\beta + \epsilon_{ijt}$. So, now only a ...
1
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0answers
49 views

Covariance Matrix of HIERARCHICAL MULTITASK GAUSSIAN PROCESS

I'm currently trying to develop a Gaussian Process to predict different levels of different individuals over time. So it is a Time Regression Problem in which we have multiple tasks, but also ...
1
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0answers
44 views

Gaussian Process regression: does there exist a conjugate prior over hyperparameters?

When adopting a fully Bayesian hierarchical setting in Gaussian Process regression is there a choice of kernel (covariance) function such that there exist a conjugate prior? If so which?
0
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0answers
22 views

Random coefficients logit estimation with Hierarchical Bayes in R

I am trying to estimate a Random Coefficients Logit model using the RSGHB R package. Thought, I came across with 2 main issues: Why the ...
1
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0answers
21 views

Covariance specification in hierarchical model

I am currently working on hierarchical models and try to get my head around the following question: What influence has the prior choice of the covariance matrix in the 2nd stage, especially when ...
16
votes
1answer
157 views

In Gelman's 8 school example, why is the standard error of the individual estimate assumed known?

Context: In Gelman's 8-school example (Bayesian Data Analysis, 3rd edition, Ch 5.5) there are eight parallel experiments in 8 schools testing the effect of coaching. Each experiment yields an ...
2
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2answers
61 views

controlling for clustering at id level in mixed effects model

I have one group ($n=40$) of subjects pre- and post-tested (time; coded $0$ and $1$) on a continuous variable (y). I also have a ...
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0answers
28 views

Mixed effect model covariance prior

How should I choose the covariance prior for my bglmer model? This is a model which has the singularity problem. ...
11
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5answers
2k views

What precisely does it mean to borrow information?

I often people them talk about information borrowing or information sharing in Bayesian hierarchical models. I can't seem to get a straight answer about what this actually means and if it is unique to ...
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0answers
13 views

Bayesian hypothesis testing with multiple beta-binomials

I want to test questions relating to whether individual ants of a certain species have personal food preferences, using a Bayesian model built up of multiple beta-binomial distributions. My problems ...
3
votes
0answers
113 views

What is the posterior kernel lengthscale of a Gaussian process?

If I have access to multiple samples from a Gaussian process with known covariance kernel but unknown parameters (i.e. unknown lengthscale), it is straightforward to estimate the lengthscale using ...