Questions tagged [hierarchical-bayesian]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
28 views

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 ...
2
votes
1answer
30 views

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] ...
2
votes
1answer
24 views

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 ...
1
vote
0answers
17 views

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 ...
2
votes
2answers
77 views

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, ...
0
votes
0answers
16 views

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 ...
0
votes
0answers
29 views

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 ...
1
vote
0answers
11 views

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 $...
0
votes
0answers
37 views

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 ...
0
votes
0answers
9 views

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 ...
0
votes
0answers
14 views

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 ...
1
vote
1answer
29 views

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. ...
0
votes
0answers
12 views

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. ...
0
votes
1answer
20 views

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)...
0
votes
0answers
31 views

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 ...
0
votes
0answers
40 views

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 ...
1
vote
0answers
23 views

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 $\pi(\theta_i|y)$ ...
1
vote
0answers
21 views

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 ...
2
votes
1answer
44 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 $\...
1
vote
1answer
19 views

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?
0
votes
0answers
13 views

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: ...
0
votes
0answers
30 views

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 ...
2
votes
1answer
36 views

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 ...
2
votes
1answer
35 views

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 ...
1
vote
0answers
10 views

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 ...
1
vote
1answer
51 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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
9 views

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 ...
0
votes
1answer
75 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 $y_t$ ...
0
votes
0answers
15 views

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 ...
1
vote
0answers
17 views

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 ...
4
votes
0answers
49 views

Why does Quadratic (Normal/Laplace) Approximation fail on multilevel models?

In Statistical Rethinking, 2nd Edition, section 13.1, Richard McElreath says: Why doesn’t simple quadratic approximation, using for example quap, work with multilevel models? When a prior is itself a ...
1
vote
1answer
91 views

How to choose a non-informative or weakly informative hyper priors for my hierarchical bayesian model?

I am learning Bayes on "Applied Bayesian Statistics" by MK Cowles. The chapter about "Bayesian Hierarchical Models" mentioned an example that we estimate a softball player’s ...
1
vote
1answer
37 views

Is there any “maximizing” in a Bayesian model?

I am not a statistician, so please bear that in mind. Suppose you have a simple model: $$ y_i \sim Normal(\mu, \sigma) \quad i = 1 \ldots n \\ \mu \sim f(\cdot) $$ where $f$ is some distribution for $\...
1
vote
0answers
55 views

Should I report the results with random effects or not (brms, re_formula = NULL vs NA)?

I am struggling to understand should I report the results with random effects or not (re_formula = NULL or NA). I have a population-based data. Patients are nested in differently sized counties and I ...
0
votes
0answers
7 views

Bayesian estimation for analysing project evaluation

Using Bayesian estimation how can we assess the group projects given that different members in the group may have performed differently?
1
vote
1answer
64 views

How to change priors in Bayesian estimation, if we get to know previous work was wrong?

Assuming we are doing a task to find how runs will be scored some match and for that, we have assumed some prior, now what if we find out midway through the process on which we built our priors was ...
1
vote
0answers
16 views

hierachical modeling of body temperature data to design thresholds for CoVID-19 testing

I am working through designing an approach to identifying temperature thresholds for CoVID-19 testing. I thought I would post my problem and see if any had recommendations. Basically, I have a large ...
2
votes
1answer
53 views

Do we estimate parameters of a prior?

I had a course of Bayesian statistics, but I don't understand it at all. I calculated a posteriori distribution and Bayesian decision rules of something like that, but I don't understand what is this ...
5
votes
1answer
82 views

Matt's trick (reparametrization) makes my models slower, not faster

I am currently programming a hierarchical model in Stan. Following the advice from section 22.7 from the Stan manual, I reparametrized my model so it samples the individual differences from a $N(0,1)$ ...
0
votes
0answers
34 views

multi-level model and hierarchical model

Are there any differences between multilevel modeling and hierarchical models? I once heard that hierarchical models is just one type of multilevel model.
0
votes
0answers
13 views

Do I use a Bayesian hierarchical regression model- problem with dependent variable

I am doing a research project for school where my dependent variable is "a response to a tweet" sentiment score (i.e. any value from -1 to 1-where 1 is completely positive, -1 completely ...
0
votes
0answers
34 views

Problems with setting weakly-informative priors

I am very new to the topic of Bayesian inferencing and I struggle with setting priors. I do understand the underlying idea of incorporating existing knowledge/prior beliefs, however, I seem to be ...
2
votes
0answers
23 views

Hypothesis testing : Constant mean over time for two conditions within an experiment

What is an approach to testing/showing that within a particular period of time, there is no change in values. So, I have my response variable measured over 30 seconds, in two conditions. I want to ...
0
votes
1answer
66 views

Can I use beta priors in zero inflated poisson model?

Please I have a two fold questions and I am not sure how to phrase the title of my post to capture both. I am trying to fit a regression model in jags, and I am new Bayesian modeling. In my model I ...
2
votes
0answers
59 views

Conjugacy in hierarchical models

I was wondering if it is possible to use conjugacy "locally" in a Bayesian hierarchical model. Locally is most likely not the right word but I'll explain the problem. For example, the likelihood of ...
0
votes
0answers
10 views

JAGS with dependent observations

I have the following model. At every time unit, the arrivals are Poisson. With a Bernoulli probability, I observe either zero of these arrivals or all of these arrivals. If I don't observe anything, ...
0
votes
2answers
85 views

Multilinear regression with nominal predictors - Bayesian

I have four nominal predictors and one metric predicted variable. I would like to know which one of predictors have more influence on the predicted variable. For doing so, I am curious to know if I ...
2
votes
0answers
49 views

Why do Bayesian hierarchical models converge where frequentist models do not?

I am analysing an experiment looking at abstinence rates among participants in a clinical drug and alcohol trial. There were two groups, those who received the new treatment and those who received ...
0
votes
0answers
60 views

How do you use multilevel regression for classification (MRP question)?

As the output of a regression model is a continuous variable, how is MRP (multilevel regression with poststratification) used to model voter classification when there are more than 2 voting choices e....

1
2
3 4 5
12