Questions tagged [hierarchical-bayesian]

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

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Bivariate/multivariate models for multinomial response variables

I need to fit two categorical (potentially correlated) response variables (each has three classes) on a set of explanatory variables, while considering for the response variables' correlation. What ...
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90 views

Marginal prior derivation in hierarchical Bayesian model

I am working on a model that is closely related to the normal gamma shrinkage prior setup discussed in Griffin & Brown (2010). Suppose we want to draw $P$ parameters $\beta_p$ with $p=1,...,P$. ...
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1answer
173 views

sampling behind bayesian hierarchical models

I'm unsure how sampling is done in Bayesian Hierarchical modelling, i'm reading a book on how to use it in PyMC3 but it doesn't explain the math and i'd like to understand it. Suppose i want to ...
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1answer
242 views

Fitting regression spline [closed]

I am reading the paper by Willemsen et al (2015), "A multivariate Bayesian model for embryonic growth", Statistics in Medicine, 34:8, 1351–1365 I have a model like $$y_{ij} = \gamma_{i2} + f((t_{ij} ...
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248 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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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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1answer
227 views

How did you learn Bayesian statistics and what would you recommend as a reliable source? [duplicate]

I'm running a Bayesian model and I'm stuck on some aspect of the model that I have difficulty to understand. Since my knowledge about Bayesian inference is limited, I would like to have some good ...
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1answer
40 views

If I have a nested multi-level model, how can I find the conditional expectation easily of the middle variable?

Suppose I have the following model: $$ y_i | x_i, V_1 \stackrel{ind}\sim N(x_i, V_2) $$ $$ x_i| V_1 \stackrel{iid}\sim N(0, V_1) $$ $$ V_1 \sim Unif(-V_2, \infty) $$ where the data is $y = (y_1, \...
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288 views

Prior Parameters in Bayesian Hierarchical Linear model

I'm trying to fit a linear model to describe student performance in 2 different schools. My response variable is $$Y_{ij}= X_{ij}*\beta+Z_{ij}*\gamma_j + \epsilon_{ij}$$ . $$i = 1,...,n $$ $$j = 1,...
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1answer
2k views

How to select hyperprior distribution for Beta distribution parameter?

I have a parameter $\theta$ whose value should lie between $(0,1)$. Therefore, I am assuming the prior distribution of $\theta$ to be a beta distribution with hyper-priors $\alpha$ and $\beta$ ie. $P(\...
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1k views

What is the empirical Bayes estimator for a gamma-Poisson with more than 1 observation for each Poisson parameter?

I am looking at the Wikipedia entry for empirical Bayes, but it's a bit confusing - it seems to me the solution must apply only to the case in which there's only $n=1$ sample $y$ for each $\theta$ and ...
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312 views

Why semi/nonparametric models?

Increasing the flexibility of models makes it prone to overfitting. On the other hand, it looks to me that, if the space function classes $\mathcal{F}$ is too big, it is hard to prove bounds on ...
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233 views

Do “true” multi-level models require Bayesian methods?

I've been recently learning about mixed effects models (e.g. via Fitzmaurice, Laird, and Ware 's book Applied Longitudinal Analysis) as well as Bayesian hierarchical models (e.g. via Gelman and Hill's ...
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2k views

Trap 66 in WinBUGS in a hierarchical Bayesian modeling

I want to analyze a multilevel multidimensional model in WinBUGS. the model is as below (N=2362 students responding to K=45 items of a test, students are nested within J=116 schools): ...
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1answer
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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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1answer
38 views

What is the difference between random-effects models, multilevel models and hierarchical models?

In the Bayesian paradigm, I have found examples of models that could be called any of the following: random-effects models multilevel models hierarchical models. Each of these categories even has ...
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1answer
58 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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1answer
63 views

Bayesian model - how to emphasize later observations?

I have a very general question, any links to relevant papers or which book I should consult should suffice. So, let's say I've got a Bayesian model (for example) to predict the outcome of a soccer ...
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1answer
336 views

Problem with “log(0)” error while using brms in R to do Bayesian analysis [closed]

I'm using brms to conduct a multilevel regression in R. I've been getting warnings and errors of the following type: ...
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1answer
51 views

Robbins estimate Empirical Bayes

From the compound sampling model where: $Y_i | \theta_i \sim Poi(\theta_i)$ The marginal distribution of $\theta_i$ is $G$, non-parametric. We get that the Bayes estimate of $\theta_i$ under ...
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1answer
71 views

re.form specifying one random effect but not the other

I have fitted a multilevel model using stan_lmer that has two sets of varying intercepts, one for categories and one for subjects. The code essentially looks like ...
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1answer
391 views

Attempting to compare Bayesian and Frequentist mixed effects models

This question may be better suited for stack overflow (happy to move it if deemed too off topic). I am currently in the process of learning Bayesian analysis using stan in R as my software. ...
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1answer
506 views

Choosing error-variance priors in hierarchical models

I am trying to find a reasonable and largely uninformative set of priors for the error variance in a multi-level model. The model was developed by others, and I am unsure whether their choices were ...
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1answer
594 views

Extending a Hierarchical Beta-Binomial Model to account for higher-level groups

I searched all over but was unable to find an answer to this question. Please forgive me if I missed something obvious. In order to analyze an experiment, I recently implemented a Hierarchical Beta-...
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1answer
88 views

Multilinear loss in Exponential-Uniform model

Let a prior $\pi(\theta)=\frac{1}{3}(\mathbb{I}_{[0,1]}(\theta)+\mathbb{I}_{[2,3]}(\theta)+\mathbb{I}_{[4,5]}(\theta))$ and $f(x\mid\theta)=\theta e^{-\theta x}$. Taking the multilinear loss $$...
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1answer
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Distributions with undefined parameters

I am studying the Bayesian Lasso and noticed something interesting on Page 682 at the bottom of the second column here Some background: a hierarchical setup for data $X, y$, regression coefficients, $...
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91 views

Meaning of “T-vector of time series values”?

I am currently studying a paper on Hierarchical Bayesian space-time models. In that, we have denoted $Y(s,t)$ to be the process of interest ate location $s$ and time $t$ in a gridded space-time. $Y(s, ...
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1answer
59 views

Deriving Gibbs sampler for specific mixture model

Let $\theta_i$ be an indicator which is $0$ if score, $X_i$, is the same for both opponents, $1$ if different: $X_i|\theta_i \stackrel{\text{ind}}{\sim} (1-\theta_i) U(0, 1) + \theta_i Beta(1, \...
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2answers
1k views

Hierarchical Multi-label Classification

I would like to make a classifier, where I can classify individuals from one hand, and from the other hand, understanding the data better, meaning figuring out which feature, is the most contributing. ...
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1answer
269 views

Stepwise regression for Bayesian models

Why isn't stepwise regression, like backward elimination, used for Bayesian models? What is generally used to find insignificant variables in bayesian methods? Or does one simply not worry about ...
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1answer
369 views

How to define function in OpenBUGS

In my Hierarchical Bayesian Model, in the data layer y[i] <- M(t,u,v)+ N[0,sigma_y] where M is a complicated function. I have generated the output of this M by ...
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716 views

Bayesian Hierarchical Model - Exact Conjugate Solution?

I was hoping to get some help. In understand how to compute an exact numerical solution (http://www.cs.berkeley.edu/~jordan/courses/260-spring10/lectures/lecture5.pdf) for the following Bayesian model:...
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488 views

JAGS meta-analysis

I'm using JAGS to run a meta-analysis and I've run into an issue. I have calculated log-response ratios and errors for about 177 studies, where studies fall into one of 8 groups. I'm interested in ...
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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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1answer
146 views

Reference for hierarchical Bayesian modelling

I am currently reading "Bayesian Data Analysis" by Gelman et al. and my main goal was to learn about Hierarchical modelling on chapter 5. I read until chapter 4 and the book is written terribly for a ...
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1answer
387 views

Parameters for a Hierarchical Multinomial Regression

I am trying to fit a hierarchical multinomial regression to cross sectional data. I have around 2000 units with only one observation per unit. I have a binomial response variable and 14 dummy ...
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1answer
162 views

Sequential Monte Carlo for hierarchical models

Does anybody know, can Sequential Monte Carlo be applied for multi-dimensional problems i.e. simulating more than 1 distribution like in hierarchical models? Maybe you know some following literature
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1answer
201 views

How to make inferences on group SD and and the SD of the group SD in a hierarchical Bayesian model?

The hierarchical model specified below is quite "standard" and easy to implement in for example JAGS/BUGS. It has an hierarchical gamma prior on the subject's precisions ($\tau_j$) which in turn has ...
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39 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, \...
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DIC to compare models with different numbers of parameter?

I am interested in comparing hierarchical Bayesian models based on the same dataset but differing in their spatial and temporal resolution. In short, I am looking at animal population changes over ...
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43 views

Gaussian process regression model for comparing two groups

I have a data set consisting of functional observations, where $Y_{mi}$ is the response of the $m^{th}$ functional observation from the $i^{th}$ group, $m=1,...,M$ and $i=1,2,$. The observations are ...
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MCMC Metropolis-Hastings sampler - Estimation of multiple parameters

First time that I ask a question on this platform! Here I go... I have a dataset with two random variables X1 and X2 and an output Y which comes from a discrete Weibull distribution. I've been trying ...
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1answer
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In hierarchical model, how to choose groups that meet exchangeability, automatically?

In hierarchical model, we assume exchangeability. For example, y[i] ~ Norm(b0 + b1[groups[i]], sigma) and b1 ~ Norm(mu_b1, sd_b1) above, all groups are assumed exchangeable. But, it might be better ...
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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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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
74 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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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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116 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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42 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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51 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 ...