Questions tagged [hierarchical-bayesian]

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

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21 views

Mixed model with panel data when some cases have constant responses (zero) over time

I have a panel data with about 300 units observed over a period of 4 weeks. In each week, I recorded a response that is a binary variable, y, for each unit of that week. For about 50% of the units, ...
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1answer
38 views

How to calculate the Jacobian of the transformation ( for covariance matrix)

I'm reading this Paper about a separation strategy for modeling covariance matrices with focus on Bayesian analysis. Direct decomposition of covariance matrix is as follows: $\Sigma = \text{diag}(S)\,...
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7 views

Setting up a hierarchical model using R2jags [closed]

I'm working on a project for an introductory Bayesian analysis course and I'm also fairly new to using R regularly. We are supposed to build a hierarchical model using a data set we found or put ...
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Posterior Predictive Check for Hierarchical Logistic Regression Model

I need to apply Posterior Predictive Check (PPC) on Hierarchical Logistic Regression Model (so I have binary outcome) to validate my model (to see goodness of fit of my model). I know that I need to ...
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Simple one way random effect model into Bayesian approach

the random effect model $y_{ij}=\beta +u_i+\varepsilon_{ij} \left\{\begin{array}{c} i=1,2,\ldots,k \\ j=1,2,\ldots,J \end{array}\right.$ Assumptions: $$\varepsilon_{ij}\ \mbox{is }NID(0,\...
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59 views

How can I derive mathematical posterior predictive distribution calculation steps for beta prior and binomial likelihood

I would like to know the mathematical calculation step by step processes with beta prior and binomial likelihood for posterior predictive distribution.
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1answer
13 views

Hierarchical Bayesian Models applications [closed]

I've been reading a bit on Probabilistic Programming (e.g. Bayesian methods for hackers) and, while fascinating, I can't seem to find many examples where such models have been used in real-world ...
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31 views

Shrinkage effects in a hierarchical model

I am working on the chimpanzees dataset from Richard McElreath's text, "Statistical Rethinking", edition 2. I have built 2 simple models, one a fixed effects model and the other a hierarchical model. ...
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How to calculate Empirical Bayes for continuous variable in Hierarchical Linear Models?

I am currently working with the radon dataset of Gelman for Hierarchical Linear Models. I have heard of Empirical Bayes and how to compute it for the Poisson-Gamma case from the data but didn't find ...
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3answers
41 views

When do we use a hierarchical model structure in Bayesian Analysis?

I am having trouble understanding when it is advantageous or when it is rational to use a hierarchical model set up in Bayesian Analysis. Basically what kinda of data do I have or what kind of ...
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37 views

How do I factor this conditional probability?

I am having a brain freeze. Could you show the steps to get from line 1 to line 2? Thanks!
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6 views

Model fit metrics for bayesian hierarchical models?

I have a hierarchical model that shrinks my individual now non independent models closer to the group level estimates. This is beneficial as it makes the inferences more robust. I have been using WAIC ...
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Adaptive MCMC when variables exist only conditionally?

I'm looking at models that make the existence of one variable depend on another variable. For example, n ~ geometric(0.5) x ~ iid(n,normal(0,1)) Here, ...
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When regularizing based on an informative prior, how to give model a little more freedom to partially reject regulariziation

I am new here I hope this question is appropriate. I am modelling a spatial domain, whereby I have repeated measures at n locations. I make a bayesian linear model at each n locations based on about ...
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1answer
47 views

Multi-level logistic regression - probability received from the intercept is different from the original sample

I am running multi-level logistic regression in order to perform case-mix adjustment (corrected estimates) for 100 clinics. I got some results but they are somehow suspicious to me. I noticed that ...
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Difference between Mixed Logit model and hierarchical bayesian logit?

I'm studying the discrete choice analysis; The utility of person $i$ for alternative $k$ is: $$U_{ik} = \beta_kx_{ik} + \epsilon_{ik}$$ where $\beta_k$ is the parameter of interest and with $\...
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How can parameters be modeled differently if they share hyperparameters?

In one popular example of multilevel Bayesian models (2007 Gelman et. al paper), radon exposure in a household is modeled as a function of the county and whether the house has a basement. In this ...
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Multivariate Bayesian Car Model Result

I have developed a multivariate Bayesian Car model for three crash severity level analysis. I found that the covariance for both heterogenous effects and the spatial effect is not significant for any ...
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2answers
83 views

Is appropriate to use empirical Bayes (EB) in this way?

Background. I have data from a study where participants make a series of judgments (a series of decisions with a binomial outcome, either $y=1$ or $y=0$). I have a model of the underlying decision-...
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1answer
42 views

Bayesian updating of a probability density for evidence on its cumulative distribution

Suppose that I have a continuous variable E as a result of a simulation, which has a probability distribution as in the figure below: As seen from the cumulative plot, ...
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17 views

Dirichlet Process mixture model with independent features

I'm trying to construct a Dirichlet process mixture model for clustering where the samples have independent features. In other words, to evaluate the likelihood of sample $x_i$, I would compute $\...
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18 views

Bayesian hierarchical model with varying scales [closed]

I would like to have a bayesian hierarchical regression model. Suppose that we have multiple data sets, which adhere to a hierarchy. Let us call the response variable in dataset 1 and 2 as $Y_1, Y_2$. ...
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1answer
43 views

How are higher level posteriors modeled in a hierarchical Bayesian model?

Hope the question isn't too naive. I've been playing around with examples from Doing Bayesian Data Analysis by Kruschke, and in the Therapeutic Touch data section there's this multi-level model ...
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22 views

Shouldn't the distribution of alpha be included in the predictive distribution of variational linear regression?

I was reading "pattern recognition and machine learning" book and I see that in the predictive distribution of the bayesian linear regression with variatioanl inference, it uses this equation $p(t|x, ...
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1answer
113 views

Conditional Probability - Mixture Model

I know that the likelihood in a p-dimensional Gaussian mixture model is given by $$ p(s|\theta) = \sum_{b_1 = 0}^1\cdots\sum_{b_p = 0}^1\left[ \prod_{i=1}^pw^{1-b_i}(1-w)^{1-b_i}\right]\phi_p(s|\mu(b,...
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Gibbs Sampling attempt at a simple Coxian distribution

I have the following Coxian model for inter-arival times ($x_i$) that has $C_x^2 < 1$: $$ p(x_i\mid \lambda,\theta) = \theta \lambda^r x_i^r e^{-\lambda x_i} + (1-\theta)\lambda e^{-\lambda x_i} $...
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ChoicemodelR - How to calculate variable importance using output of ChoiceModelR?

i have built a HB choice model using ChoiceModelR. Can someone tell me how to calculate the Relative Variable Importance from the output?
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30 views

Statistical model suggestion for binary decision problem

I am looking for a statistical/machine learning model, which can describe and predict a (forced) binary decision between say A and B at any moment in time. I have input data from time series of say 3 ...
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1answer
45 views

Bayesian Inference: Prior in Chinese Restaurant Process

For the Chinese restaurant process, as used in Dirichlet Process mixture models, we have a prior that data point i belongs to cluster j, where c is an indicator. n represents the total number of data ...
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61 views

Proposal for correlation matrix with LKJ prior

I am writing a Gibbs sampler from scratch. As recommended in various places (http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n416.pdf, and in another question Covariance matrix proposal ...
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24 views

Shape of parameters marginal posterior in hierarchical Bayes model

Consider a generic hierarchical Bayes model with data $y_i\sim p(y|\theta_i)$, dependent of parameters $\theta_i\sim p(\theta|\phi)$ and hyperparameters $\phi\sim p(\phi)$. Furthermore, assume that $\...
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Bayesian estimation of mixed effects models covariance matrix

For a mixed model of the form: $$Y = X\beta + Z u + \epsilon$$ I know it is usually assumed in the parametric approach that: $u \sim N(0, D)$ and $\epsilon \sim N(0, \sigma^2I)$ Where $D$ is a ...
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19 views

Derivation of a Bayesian predictive probability

Suppose a random variable $Y$ is governed by an unknown parameter $p$. From a set of observations $X$, I want to draw the probability of $Y=y$. How can I compute the Bayesian predictive probability $f(...
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18 views

Wrong sign of a model coefficient in Bayesian Poisson-Lognormal Car model

I am trying to develop a multivariate Poisson lognormal CAR model. One of my most important variables in the model is providing a negative sign which should be positive. However, when I develop a ...
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1answer
22 views

Derivation of posterior for Bayesian hierarchical models

In Bayesian hierarchical models, the following posterior is used: $$p(\theta,\phi|y)\propto p(y|\theta)p(\theta|\phi)p(\phi)$$ I'm trying to derive this myself but when I use Bayes' rule, I get the ...
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1answer
17 views

What are the necessary qualifications or assumptions to say that a graph structure is a Markov Chain?

I have a graph structure and want to say it is a Markov Chain. But I am wondering what necessary assumptions or properties that my graph structure need to meet to be called a Markov Chain?
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29 views

Use zeros trick for modeled parameters

Can the zeros trick be applied for specifying a new distribution for modeled parameters such as a varying intercept model? I am trying to estimate a hierarchial model (like the following) where I have ...
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27 views

Probability distribution of the standard deviation of a gamma distribution

I want to generate some data using a series of Gamma distributions in a Bayesian hierarchical setting. I need to generate the data for a series of contexts, but I got only 2 data points per context, ...
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75 views

Mixed Effects, Doctors & Operations: predicting on new data containing previously unobserved levels, and updating our confidence accordingly

Here's a quick sketch of a hypothetical situation. There are Doctors $\{1, \ldots, J\}$ who perform different types of operations $\{1, \ldots, K\}$. Our response variable is whether the operation ...
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8 views

Pseudo T-stat in Winbugs?

I am trying to obtain the "Pseudo T-stat" in Winbugs for a Poisson Log-normal model. Any suggestion of how can I get that.
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1answer
50 views

Hierarchical bayesian model without packages

I'm attempting to build a hierarchical Bayesian model. For various reasons (including my own edification), I want to do this from scratch (i.e., without using the various packages and libraries ...
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39 views

Winbugs code multivariate hierarchical Poisson Log-normal CAR model

I am looking for some example code to develop multivariate hierarchical Poisson Log-normal CAR model using Winbugs. Can anyone help me with similar reserach that added their code? Also, how can I ...
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50 views

Metropolis-within-Gibbs for parametric inference of a regressive model

I have a regressive model of this form \begin{equation} y=f(\theta)+\varepsilon \end{equation} to describe observations $y$, with noise $\varepsilon$ and a parametric function $f$ with parameters $\...
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32 views

Statistical Significance for Bayesian parameter estimation

I was reading a paper that estimated parameter using the Bayesian method. I am wondering how they can write the following statement based on the table below "Two lane indicator is found to be ...
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0answers
11 views

Hierarchical simulation of patient waiting times in order to keep annual average below some threshold

I have a dataset about patient waiting times in a healthcare district. These data have 3 categorical variables: - healthcare provider; - healthcare service (eg. cardiology visit, electrocardiogram, ...
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65 views

Multilevel Negative Binomial fails with MLE

I have a pretty complex multilevel neg. binomial regression that does not converge when using a regular MLE (but from what I understand, when dealing with multilevel models, MLE is not regular, per se)...
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12 views

Weight of data vs. likelihood

I'm fitting a Bayesian multi-level model with an optional quantity of data (1 year, 5 years, 10 years, etc. of observations), and I have the option to include all of the data or less, does it ever ...
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2answers
58 views

Selecting informative priors

I am questioning myself on how to chose the priors for a bayesian analysis in Rstudio. I'm trying to investigate the chances of relapse in a set of patients. These patients are all affected by a ...
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1answer
90 views

“Mean” & “median” comparison and zero variance confusions when making inferences in Bayesian model

Background: In Chapter8 of this great book, the authors build a Bayesian model and use to show the posterior distributions of the latent state $N_{t}$ and its credible intervals. The model is ...
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45 views

Bayesian hierarchical coin flip model

My question is: what is the marginal probability $P(x_1, x_2, \dots, x_n | y_1, y_2, \dots, y_n, \alpha, \beta)$ or $P(X|Y, \alpha, \beta)$? in the following model: $\phi \sim \text{Beta}(\alpha, \...