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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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7 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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11 views

Bayesian parameter estimation with varying subsets of data?

I'm currently working on a model in which I have 2 measurements, taken at different temperatures. The covariance between these measurements with temperature is assumed to be linear and therefore a ...
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20 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(...
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1answer
21 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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15 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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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 ...
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1answer
35 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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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
47 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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19 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 ...
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1answer
57 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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11 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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12 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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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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14 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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9 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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22 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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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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39 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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39 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 ...
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2answers
256 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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21 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 ...
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1answer
52 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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33 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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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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58 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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33 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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13 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 ...
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1answer
66 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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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 ...
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1answer
74 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)\\ \...
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34 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 ...
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36 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 ...
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0answers
47 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 ...
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34 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?
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21 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 ...
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20 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 ...
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136 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 ...
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2answers
55 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
26 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. ...
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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
11 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 ...
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0answers
90 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 ...
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1answer
40 views

Interpretation of posterior distribution for Gelman's Rat Example

Introduction Chapter 5 of Bayesian Data Analysis 3rd Edition uses an example of rat endometrial stromal polyps to illustrate the concept of hierarchical regression. In particular, Gelman and ...
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1answer
55 views

What is the connection between Bayesian Model Averaging and SSVS?

What exactly is the difference between Bayesian Model Averaging (BMA) and the Stochastic Search Variable Selection (SSVS) prior when we talk about linear regression models? The SSVS prior is used ...
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0answers
39 views

Excellent fit, zero convergence hierarchical dirichlet model in JAGS

I am fitting a hierarchical dirichlet model to some data in JAGS. My samples (referred to as cores in the code) are observations of the relative abundance of 3 ...
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0answers
39 views

Bayesian Regression with LASSO

I am trying to build a Bayesian regression model with LASSO regularization. My understanding is that I can do this by setting a Laplace prior on the coefficients. I also need a prior for the variance ...
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0answers
69 views

How to infer a prior belief after observing a behavior

My participant goes through a maze made of 32 T intersections. At each intersection he must choose whether to go either to the left or to the right: one option will lead to another T intersection, ...
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0answers
38 views

using rstanarm for quantile regression

I understand that rstanarm can be used for GLMs, GAMs and hierarchical models. Does anyone know, if I can use it to estimate quantile regression models? If not, are there other Baysian R package, ...
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0answers
25 views

Uninformative priors for variance distribution in hierarchical bayesian models

I read that uninformative priors for population variances are often represented by invgamma(eps,eps) where eps could be 1, 0.1 or 0.001. In my model I used these but variance sometimes goes upto ...