Questions tagged [hierarchical-bayesian]

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

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Signs of estimated coefficients using Bayesian Poisson regression and Hierarchical Poisson regression

For poisson regression, I used the formula Y~ v1+ v2+ v3+ v1$*$v2+ v1$*$v3+ v2$*$v3, i.e. the main effects plus the interaction terms. I have used Metropolis algorithm and variable selection on the ...
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Analyzing the variance of an outcome variable: modelling standard deviation/sigma itself

Is the following a correct approach for sigma modelling? Let’s assume we have a Y variable named hours in lognormal scale. We would like to know how these hours changed in time (variable named year). ...
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Transforming log-scaled splines regression outputs to an understandable scale

Please give me some advice. I am using brms package and mgcv package for two regression models: bernoulli lognormal The problem is that both of these models outputs are in lognormal scale. As much ...
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Accounting for multiple layers of uncertainty in a model

Let's say I have data on 10 stores that sell widgets, each of which received num_orders number of orders in a certain timeframe, and sold a total of ...
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May Skilling's Nested Sampling Estimate parameters in hierarchical model?

May Skilling's Nested Sampling integration technique Estimate parameters in hierarchical model?
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Lognormal model: reporting median or geometric mean

I have a bayesian lognormal model as follows (brms package): m = brm(y ~ 1, data = df, family = lognormal) Model was run with default priors. This is model's ...
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R Stan: Rejecting initial value error only with real data, not with simulated data

I am trying to fit a non-linear function to a dataset using Stan and R. I tested my model with a simulated dataset. It works nicely. However, as soon as I use real data that is formatted exactly the ...
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Bayesian Hierarchical Models with different group sizes of crossed random effects

I have some abundance data for sites taken over a series of years. Some sites are missing data for some years and some sites only started being recorded several years in. I'm interested in the factors ...
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How to obtain a generalized bayes estimator when we have random sample from the uniform distribution with a Pareto prior and a improper hyperprior?

Let $\boldsymbol{X}=\left(X_{1}, \ldots, X_{n}\right)$ be a random sample from the uniform distribution on $(0, \theta),$ where $\theta>0$ is unknown. Let $$ \pi(\theta)=b a^{b} \theta^{-(b+1)}, a&...
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Correct specification of a hierarchial model for analysing temporal trends

My data has a nested structure, which is suitable for hierarchical modelling. The categorical variable used as a hierarchical level is county. As the counties are unequally sized (different number of ...
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Behaviour of the marginal in the limit for an infinite sequence of hierarchical priors

Consider the following model: $$y \sim \text{Exponential}(\lambda_0) \\ \lambda_i | \lambda_{i+1} \sim \text{Exponential}(\lambda_i+1) \\ \text{for } i=1,2,\dots,d\\ \lambda_{d+1} = k $$ With an ...
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When to stop the chain of priors in Bayesian hierarchical models?

From Wkipedia's article on hyperprior: In Bayesian statistics, a hyperprior is a prior distribution on a hyperparameter, that is, on a parameter of a prior distribution. There will be some ...
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How can PyMC3 handle uncertainty in the number of parameters in a Dirichlet Distribution?

I'm taking a look at the following to familiarize myself with Bayesian Inference in PyMC3: https://towardsdatascience.com/estimating-probabilities-with-bayesian-modeling-in-python-7144be007815 In this,...
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Discrete choice utility/Probability of choice for Dual Response - No Choice

I am ran a Choice based Conjoint analysis, where I provided a Dual Response - No Choice. So after choosing the preferred product out of 3 alternatives, I asked the participants if they would actually ...
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minimum amount of prior to get a mixed-model to converge (in R)

This may be a simple/naive question, but I have a non-converging lmer() model due to singularity of its random covariance matrix. I was wondering what is a possible ...
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Bayesian Regression Estimates

Hi I am new to Bayesian Regression, I wanted to understand why would the Bayesian regression give exactly the same results as the priors supplied? I tried running a bayesian model on 10% of the data ...
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Testing over- and underfitting on bayesian regression models using stan (brms)

How you guys test models' over- and underfitting? Could you please name some ways to do it. Package I am using: brms: Bayesian Regression Models using 'Stan': https://cran.r-project.org/web/packages/...
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Bayesian Regression Model

I am new to Bayesian modeling. I am running Bayesian regression model in R using brm function from brms library, which is powered by STAN. I have a data with 10 million records. I took 10% sample out ...
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Bayesian Decision making with a mixed effects model

Background A company runs an AB test in which the unit of randomization (the customer) can interact with the variant several times throughout the experiment. The outcome is a binomial random variable ...
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Hierarchical Categories as Input Features

I have a regression problem. Two input features describe a category and subcategory. For illustrative explanation, let's consider we speak about city and district. Some more details about the ...
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Ranking Prediction Intervals - Multiple Comparisons?

I fit a model that tries to match the personality of sales reps to customers based on demographics. It's a hierarchical bayesian model that predicts the probability of conversion with sales rep[i] ...
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1answer
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Population-wide county-based data: reasonable to report temporal trends using hierarchical modelling?

I have a population-wide data, including county-level information. Subjects are unequally distributed between the 10 counties in the dataset, resulting in multifold differences. The problem is that ...
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Why do we reparameterize before assigning a hyperprior distribution?

I am studying hierarchical models, and trying to understand a point in the book where they try to decide on a non-informative hyperprior distribution. The hyperparameters is $\alpha$ and $\beta$ for a ...
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Conditional independence assumption in hierachical models v.s. i.i.d. assumption of data

In a hierachical model, we have $$p(x_1, \dots, x_N, z_1, \dots, z_N, \beta) = p(\beta) \prod_{i=1}^N p(z_i | \beta) p(x_i | z_i) $$ In such models, we have $x_i \perp x_j | \beta, i \neq j$. However, ...
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Does Central Limit Theorem have anything to do with Bayesian Inference? [duplicate]

I am studying Central Limit Theorem and Bayesian Statistics and got a question that which or what part in Bayesian Statistics the concept of Central Limit Theorem is applied. If so, I'd like to know ...
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What value of thinning is acceptable in Bayesian data analysis?

I am running a poisson regression in rjags. I observed that my trace plots do not converge very well when I use a thin=10 but they all do converge pretty well when I use a thin=1. What is the ...
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What is a maximum asymptotic level parameter?

I am currently studying the model described in this study for estimating the COVID19 deaths. Their model is a Bayesian, and is fairly simple. Let $Y_1, Y_2, \ldots Y_n$ be the number of deaths on day $...
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Should I report credible intervals based on HDI or QI?

I have highly positively skewed outcome variable. I need to publish my results in an academic journal. tidybayes allows calculating credible intervals (CI) using median or mean with high density ...
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Difference between Infinite HMM and Latent Variable Model with Sequential Chinese Restaurant Prior?

What is the difference between an infinite HMM (http://mlg.eng.cam.ac.uk/zoubin/papers/ihmm.pdf) and a latent variable model where the latent states are given by a distance-dependent Chinese ...
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Difference between p(t,alpha,beta|y) and p(t|alpha,beta,y) Hierarchical model example from Gelman

The question surely has broader relevance, however it has come to me while studying 5.3 Bayesian analysis of conjugate hierarchical models of Bayesian Data Analysis (3rd edition) by Gelman. t will ...
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Polynomials in a regression model (Bayesian hierarchical model)

I am not a trained statistician and am looking to get some clarification of a model from literature. The study in question is `A Hierarchical Framework for Correcting Under-Reporting in Count Data. ...
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Modelling uncertainty at both the individual and population level with beta-distributions

I want to measure the distribution of a population's performance on a test. Each person takes a version of the test with a random selection of N questions from a large pool of possible questions. ...
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What is the probability that a parameter is greater than other parameters given we know the posterior distribution

Suppose that we have have some form of compositional data $x_i, i\in[1, n]$ which we propose comes from a Dirichlet distribution such that $$ x_i \sim \mbox{Dir}(\lambda \alpha),$$ where $x_i=(x_1^{(i)...
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Is it statistically valid to use K Means to cluster fitted respondent part worth utilities from Conjoint Analysis(Hierarchial Bayes Multinomial Logit)

Introduction: My team used Conjoint.ly to run a conjoint analysis survey to do market research. From https://conjointly.com/guides/conjoint-technical-notes/: Conjoint.ly estimates a hierarchical ...
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How to estimate the point mass portion of the spike and slab priors?

I am new to Bayesian variable selection. In Bayesian one of the popular method of doing variable selection is using spike and slab priors. The spike and slab priors have this spike component and slab ...
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Bayesian hierarchical model - exercise

I have to solve a bayesian statistics problem like a follows $y_i$ distr as $Bin(n_i, \theta_i)$ conditional on $\theta_i$ I observe several $n_i$ and $y_i$ and I’m interested in $\pi(\theta_i|y)$ ...
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How to model proportions with a hierarchical structure?

I have thinking about how to model proportions for a problem with hierarchical structure. In the problem, I have observations of users over multiple days, where each observation is a proportion of ...
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1answer
39 views

Approximation in hierarchical model

Consider a simple Bayesian hierarchical model: $y | \theta \sim P(y | \theta)$ $\theta | \phi \sim P(\theta | \phi)$ $\phi \sim P(\phi)$ I'm interested in drawing from the posterior distribution of $\...
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Bayesian estimation difference between inferences is conjugate prior and non informative prior [duplicate]

What are the differences in the inferences using non-informative (specifically Jeffrys) priors as compared to the conjugate prior?
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How can I model a set of related opinion polls that I ran on Twitter?

So I've been running some sports-related polls the last couple weeks on my Twitter account. Specifically, I am asking for opinions on NBA prospects. The poll looks essentially like this: ...
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Posterior mean of $\mu$ in Bayesian Hierarchical model (Poisson-Gamma)

Chapter 7 of Jim Albert's book considers the case of using a hierarchical model, to estimate heart-transplant mortality rates ($\lambda_i$) from 94 hospitals, each with it's own exposure (# of ...
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Normalizing posterior distribution

This is from task 5.3. in Bayesian Data Analysis 3rd edition by Gelman et al. It deals with a hierarchical model where I am supposed to simulate the posterior distribution for $\tau$, which is the ...
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1answer
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How to factor this conditional probability?

In chapter 5.4 in the book Bayesian Data Analysis by Gelman et al. I see the following expression related to a hierarchical model: $$p(\mu,\tau|y) \propto p(\mu,\tau)p(y|\mu,\tau)$$ How do I derive ...
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Group level distribution for positive parameters in Bayesian multilevel models

I am doing a lot of modeling with models that require some parameters to be positive by design. However, I am struggling to figure out which approach works best when I try to use multilevel modeling ...
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49 views

Exploding probability under simple hierarchical Bayesian formulation

I am wondering if someone here can clear up a point of confusion that I have when applying MCMC or an optimization method to hierarchical Bayesian problems. Let's say we have a likelihood and prior ...
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How to obtain equation for evidence given equation for joint density of latent and observed variables (Variational Inference)

I am working through the following review paper: https://arxiv.org/pdf/1601.00670.pdf and would like to gain some insight into arriving at the formulae for joint density of latent and observed ...
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Ideas how to report/emphasize a non-linear effect in abstract as text in case of no p-values?

I have a result that needs to be noted in abstract as this is important. I use Bayesian regression modelling and I have non-linear? effects as shown on plots below, what is a good way for reporting it ...
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48 views

One-step ahead predicitons in a Bayesian state-space model

How can I make one-step ahead predictions in a Bayesian state-space model? Specifically, for the model \begin{align} y_t \sim& N(x_t, py) \\ x_t \sim& N(rx_{t-1}, px) \end{align} where $y_t$ ...
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Hierarchical model with a different set of covariates by group

I'd appreciate any good reference material on specifying a hierarchical model with a different set of covariates by group. Textbooks usually reference varying intercepts and slopes, but in my real ...
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How to model repeated measurements with the same outcome in a Bayesian framework?

Can't think of a more accurate title, so I'll illustrate the problem with an example. I want to record temperature using cheap noisy sensors. I also have recordings from a gold-standard reference ...

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