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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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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 ...
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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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49 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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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?
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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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1answer
35 views

Multi-level models and residuals

As one increases the number of levels in a multi-level model, should one expect the output model variance to go down? That is, as we increase levels in our model: Full pooling: $y_i \sim \text{N}\...
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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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1answer
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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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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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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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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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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(...
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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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1answer
67 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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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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211 views

Bayesian Modeling: Yes, No and Maybe Responses

Respondents replied in the following way: Yes: they will be attending No: they won't be attending Maybe: they attach a percentage certainty as an estimate that they'll be attending. E.g. 40% sure ...
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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
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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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
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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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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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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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2answers
5k views

What prior distributions could/should be used for the variance in a hierarchical bayesisan model when the mean variance is of interest?

In his widely cited paper Prior distributions for variance parameters in hierarchical models (916 citation so far on Google Scholar) Gelman proposes that good non-informative prior distributions for ...
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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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1answer
178 views

Data Conversion to Standard data format in hierarchical Dirichlet process

I'm trying to test the performance of posterior inference on a set of documents with hierarchical Dirichlet process for topic modeling. How can i convert my data (document) to standard data format ...
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1answer
205 views

How can I identify market regimes with a Hidden Markov Model?

I am trying to identify market regimes (2 states: bull or bear) with percent changes in equity returns. Can you help me in the mathematicl modeling of this? So far, I thought that for each day, there ...
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221 views

Variational Bayes for Multivariate Normal distributed data with shared mean and precision

I have a model represented in graphical model and part of this model states that there are N data points that are generated from multivariate normal with shared mean vector and covariance/precision ...
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2answers
2k views

Normalizing constant irrelevant in Bayes theorem?

I've been reviewing Bayesian literature in an attempt to utilize Bayesian inference for hypothesis testing when I have very well established priors, but there's one thing I cannot get my head around: ...
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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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1answer
1k views

How to interpret the output of choicemodelr (rhierMnlRwMixture) in R

My Problem I just started using the R library choicemodelr and succeded in getting some beta values as a solution. But I wonder how do I assign these values to the ...
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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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1answer
231 views

Using PyMC3, how could I force a maximum to posterior distribution?

I am pretty new to bayesian statistics and PyMC3. I am doing a hierarchical model where the output variable I am trying to predict is a percentage with a maximum of 100%. My problem is that my ...
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1answer
235 views

Comparing top level group effects using a 3-level hierarchical regression

I would like to detect group effects (if any) along with statistical confidences. I have a hierarchical data set structured as follows: Drug Groups ...
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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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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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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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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 ...
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2answers
310 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 ...
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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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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
259 views

How to specify the Bayesian version of a clustered-robust standard error OLS in BUGS/JAGS or Stan?

I am trying to reproduce a simple OLS model fitted with clustered-robust standard errors within the Bayesian framework (be it with BUGS/JaGS or with Stan). In R, my frequentist model is the following:...
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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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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 $...
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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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1answer
257 views

Bayesian inference on mean of statistic from population

Suppose that a collection of time intervals $t_i$ have occurred, for $i=1,...,n$. These should be considered as samples from a population governed by some distribution. During these time intervals, ...
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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 ...