Questions tagged [hierarchical-bayesian]

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

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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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221 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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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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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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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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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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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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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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249 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

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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37 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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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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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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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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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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“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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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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269 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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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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Hierachical Bayesian Linear Regression using PyMC3 is super slow [migrated]

I am trying to write some code for implementing HBM in the case of logistic regression using the adults dataset from the UCI repository. I have already written the code, but sampling is super slow, ...
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Determine hyper-prior for gaussian distribution from existing data [closed]

Not sure how to determine hyper-prior for prior distributions, specifically using historical data. First what I am doing: I want to estimate parameters for a normal likelihood function using Bayesian ...
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Normal-Gamma: Metropolis-Hastings on log-scale, but no Jacobian?

I am reading the paper by Griffin and Brown (2010) where at one step in their MCMC procedure they need to sample from the following conditional posterior: $$ p(\lambda|\gamma, \Psi)\propto \pi(\...
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joint model and multivariate model

I have a crash data set which provides information about the frequency of crash by severity level on each intersection. I want to develop a joint model for frequency by severity. I am new in this ...
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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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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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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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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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Using marginal likelihood for weighting in bayesian hierarchical model?

I have data from a series of experiments. I have a simple model for generating the data these experiments which allows me to estimate a parameter. Some experiments do not conform to my model and ...
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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
32 views

deriving likelihood function for hierarchical bayesian model

I'm struggling with hierarchical bayesian modeling. I need to derive a full likelihood function for the given hierarchical structure of the model. $a_{it}|\lambda_i\sim TN(\lambda_i,\beta)$ $x_{it}|\...
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1answer
354 views

Hierarchical bayes

I am programming in R using hierarchical bayes for a choice-based conjoint task and wondering how I code the "none of the above" option in the design matrix? The <...
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1answer
498 views

Relation between Bayesian analysis and Bayesian hierarchical analysis?

I have been studying a Bayesian hierarchical model. In that model all I am dealing is with the estimation of parameters. In Bayesian analysis, loosely speaking, we update our prior knowledge (in light ...
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what is the difference between a multilayered autoencoder and a hierarchical latent variable model?

I have been trying to understand how hierarchical latent variable models are different from multilayered autoencoders and in specific the argument below Autoencoder networks resemble in many ways ...
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24 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 ...
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25 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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67 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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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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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
48 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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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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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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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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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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33 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
33 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
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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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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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 ...