Questions tagged [hierarchical-bayesian]
Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions
0
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0answers
16 views
Bayesian chi-squared tests
I have a dataset with two groups of participants. Each participant performed a repeated measures task on which three types of errors could be made. I want to measure the difference in distributions of ...
2
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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
51 views
How to choose the best method to generate random values [closed]
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
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 ...
2
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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 ...
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
31 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 ...
1
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0answers
28 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
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 ...
2
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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
votes
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
69 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 ...
0
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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 ...
0
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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 ...
1
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0answers
30 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
16 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
58 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
votes
2answers
313 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
30 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
vote
1answer
55 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 ...
0
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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
72 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 $...
1
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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 ...
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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 ...
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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)\\
\...
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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
45 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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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 ...
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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
158 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
votes
2answers
63 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
116 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 ...
1
vote
1answer
45 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 ...
