Questions tagged [hierarchical-bayesian]
Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions
707
questions
0
votes
0
answers
6
views
Bayesian Hierarchical Clustering prior update
I am working through Heller and Ghahramani's "Bayesian Hierarchical Clustering" paper (https://www2.stat.duke.edu/~kheller/bhc.pdf) and things aren't quite working out the way I expect with ...
0
votes
0
answers
44
views
+100
Posterior Distribution in a Bayesian Multivariate Normal Model
I am currently working on a Bayesian inference problem and would appreciate some help on computing the posterior distribution of a hyperparameter within a specific multivariate normal model. Below, I ...
- 105
1
vote
0
answers
25
views
Bayesian hypothesis testing using posterior samples of estimated parameter
I'm modeling recruitment curves using a Hierarchical Bayesian model. There is a key parameter in my recruitment curve, let's call it $P$. I have two groups (A and B) of participants of respective size ...
- 11
0
votes
0
answers
16
views
Difficulties with estimation and strange fitted values for BVAR (BVAR R package)
I'm using the BVAR package in R to estimate a Bayesian vector autoregression involving the following monthly variables:
US Capacity utilization, US Total Employees, US PCE index, and 5,10,20,30 year ...
1
vote
1
answer
25
views
Determining the number of interactions between the independent variables
I am trying to use GLMMs models to analysis the morbidity status of child (yes or no) with mother’s demographic and environmental factors like
Wealth with factors ("Lower quartiles”,"...
2
votes
1
answer
26
views
The "Multiple Error Terms" notation for hierarchical models
I'm seeking clarification regarding notation for Bayesian hierarchical models, specifically the mixed effects model. Consider the following hierarchical model for the outcome of unit $i \in N$ in ...
- 731
1
vote
1
answer
24
views
How can a Bayesian linear hierarchical random intercept model with normally distributed priors for coefficients represent a non-normally DV?
Suppose you have a hierarchical random intercept model with a dependent variable that is zero inflated. The link function is linear and the priors for the coefficients are normally distributed. In ...
1
vote
0
answers
33
views
Does a variance decomposition make sense with a non-linear link function?
I am doing a variance decomposition, with a hierarchal random intercept model like the one below (BRMS R Code):
...
0
votes
0
answers
6
views
Alternatives to spatial and temporal aggregation of time series to discover more learnable patterns
Given taxi demand time series of towns in a country. I would like to do demand forecasting.
I noticed that when the town's time series is zero inflated the prediction is poor. However, when these ...
- 244
0
votes
0
answers
48
views
Using Bayesian statistics in time series forecasting
I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting.
Given hierarchinal ...
- 244
1
vote
0
answers
33
views
Bayesian hierarchical exchangeability assumptions reasonable with a check treatment?
This is information I believe to be true
A practical feature of hierarchical Bayesian models is that partial pooling reduces (eliminates?) the need of adjusting for multiple comparisons when ...
1
vote
0
answers
32
views
Proper analysis of completely crossed design with subjects and items as random effects (brms)
I have the following study design:
stimuli: 240 pictures:
6 pictures of 40 students each
(each student fixated one of six points and during each fixation one picture was taken)
each stimulus was ...
- 11
0
votes
0
answers
42
views
Calculate posterior distribution and full conditional of a HMM
Set up a Bayesian analysis of an hidden Markov model and calculate the posterior distribution and the full conditionals, given this assumptions:
The state space of the hidden process has size m
$Z_t|...
5
votes
1
answer
125
views
Doing empirical Bayes with improper prior - marginals that do not exist?
I am considering a Bayesian linear model for which the prior is not proper.
The model is as usual $y = X \theta + w$ where $w \sim N(0, \sigma^2)$, and $\theta, \sigma^2$ are unknown.
The distribution ...
0
votes
0
answers
5
views
Criterion to assign individuals to clusters in bayesian mixed model with distribution of probabilities
I have a dataset with a set of individuals indexed by $i = \{ 1, ..., N \}$, and I make a number of measuremenets under two conditions for each individual to measure the effect $\beta$ of my ...
- 1,027
0
votes
0
answers
25
views
Best way to show one Bayesian model is more certain and accurate than another, based on simulated data?
I'm trying to compare performance of two bayesian models $A$ and $B$ on simulated data. It's a recruitment curve fitting problem and I'm interested in how accurate these models are in estimating only ...
- 211
0
votes
0
answers
25
views
Inference of Beta-Bernoulli Distribution
Assume $x_1, x_2, \cdots, x_n$ follows a $Bern(\pi_0)$, Let $y_{ik}$ follows $Beta(\alpha,\beta)$, $i\in \{1,\cdots, n\}$, and $k\in \{1,\cdots, K\}$. Let $z_k$ follows a Bernoulli Distribution with a ...
- 1
0
votes
0
answers
31
views
Hierarchical models: Estimating variance and combining two estimators
Assume that $y_i \sim N(50,10)$.
I observe a signal with additive Gaussian noise $s_i \sim N(y_i, \sigma_d^2)$
I observe $n$ such signals, each corresponding to a different $y_i$.
I want to estimate $\...
- 1
1
vote
0
answers
39
views
In Bayesian modelling how to interpret hierarchical hyperparameters with regards to "borrowing"?
With regards to hierarchical models I often see these referred to as groups borrowing information from each other e.g.
It will be seen that the hierarchical model posterior estimates for one school ...
- 698
0
votes
0
answers
12
views
In my mixed effects model, are the confounded MCMC chains between my random intercepts and my global intercept problematic?
I implemented an MCMC algorithm for the following regression model:
$$y_i \sim N(\mathbf{x}_i'\boldsymbol{\beta} + \eta(\mathbf{s}_i) + \theta_i,\sigma^2),$$
$$\boldsymbol{\beta}\sim N(\boldsymbol{0},...
- 1,819
0
votes
0
answers
36
views
Is it possible to get the statistical significance of the mean of a distribution inferred through a Bayesian Approach?
I am new to Bayesian inference and I am not sure if this problem and question are well-posed.
When estimating the coefficients of a linear regression we can evaluate the statistical significance of ...
- 111
0
votes
0
answers
47
views
What is the trace in a Bayesian Model?
I am studying a python library that uses Bayesian inference to identify the coefficient of a linear regression.
I have two questions, one very broad and one more vertical on MCMC and numpyro.
What is ...
- 111
0
votes
0
answers
19
views
Is it okay to merge seperate MCMC chains, using different seed value? [duplicate]
I'm new to Bayesian analysis. I'm trying to estimate species's abundance.
As I know, when using MCMC sampling, it is recommended to make more than three chains. However, the function I use can make ...
0
votes
0
answers
44
views
Bayesian estimation for a ranking outcome variable
I'm interested in modeling how a ranking depends on a continuous feature. I have many related groups of these rankings, so I want to use partial pooling with the usual Bayesian machinery, but I'm ...
- 101
0
votes
0
answers
17
views
Cluster based on random effects, STAN
I have a problem where I measure repeated responses in condition A and in condition B for a set of individuals $i=1,...,n$. I am interested in learning about the effect of the condition in the ...
- 1,027
0
votes
0
answers
5
views
Finding subgroups in population, using individual effects of hierarchical model
I want to know how to look for effects both at a population level, and at an individual level in an experiment. I was wondering if I can do this with hierarchical Bayesian models as follows.
In a ...
- 1,027
2
votes
0
answers
69
views
A hierarchical model with conjugate hyperprior
I have a modeling problem that I am trying to formulate in a Bayesian manner to do inference.
Basically, I have a prior where the variance is unknown, and we want to treat it as uncertain (though with ...
0
votes
0
answers
63
views
Ways to include time in hierarchical mixed effects model
My colleagues and I have been using a hierarchical mixed model that so far has provided good predictions. As time goes on, however, it's clear that not including time as a factor in the model degrades ...
- 2,574
1
vote
0
answers
42
views
How to solve for an unkown probability distribution within a hierarchical model?
The Problem
Given probability distributions $P(\theta)$ and $P(X)$, and given an inverse function $Y=f^{-1}(X,\theta)$ that returns a unique $Y$. How can one estimate the unkown distribution $P(Y)$ in ...
- 11
0
votes
0
answers
22
views
How to structure a multi-level model for a five-a-side football problem
I'm working in an unfamiliar Bayesian context here, so apologies if my terminology isn't entirely correct!
Imagine I'm trying to predict the performance of players on a of a five-a-side football team. ...
- 11
0
votes
0
answers
46
views
Normal-Normal mixture model for variance hyperparameter
Consider the product of two Normal distributions (prior-hyperprior):
$$
p(\sigma^2) \propto \mathcal{N}(\theta; 0, s^2 \tau^2 \sigma^2)\mathcal{N}(\sigma^2; 0, c^2 \gamma^2)
$$
this is a scale mixture ...
- 43
0
votes
0
answers
37
views
Advice for modeling variance in a hierarchical linear model
I have a dataset of longitudinal measurements for different sample individuals, with some covariates such as age, sex, time period, etc. The number of measurements taken for each individual varies. I ...
- 564
1
vote
1
answer
49
views
How can I marginalize $\boldsymbol{\alpha}$ out of my hierarchical model?
Suppose I have the following hierarchical distribution:
$$\mathbf{y} \sim \text{Normal}(\mathbf{X}\boldsymbol{\beta} + \mathbf{K}\boldsymbol{\alpha}, \sigma^2\boldsymbol{\Sigma}_y),$$
$$\boldsymbol{\...
- 1,819
2
votes
0
answers
135
views
Bayesian meta-analysis: Why and how to weight individual study's contribution to overall effect?
I'm interested in performing a Bayesian meta-analysis, specifically, using a random-effects hierarchical model (as described here). Briefly, in this model we assume that the $k$th study's reported (...
- 43
0
votes
0
answers
37
views
How multilevel Bayesian models handle group imbalance
I’ve read that partial pooling (multilevel / hierarchical models) can balance the extremes: on one hand, zero pooling where every group receives its own parameters, non influenced by other groups. And ...
- 2,501
1
vote
0
answers
110
views
Bayesian Hierarchical Regression Models for Panel Data
I am fairly comfortable with Bayesian hierarchical regression models, but I am new to panel data analysis. As someone from the social sciences, I have found that the majority of resources on panel ...
- 137
2
votes
1
answer
223
views
brms model specification with 3 (crossed or nested?) levels
I have a data set that looks like this toy data
...
- 23
0
votes
0
answers
39
views
Conditionally conjugate prior for non-nested (i.e. crossed) normal model?
I am trying to write/understand a conditionally-conjugate Gibbs sampler for what is essentially a linear, mixed effects model. I more or less get the conditionally-conjugate posterior for the ...
- 101
0
votes
0
answers
25
views
Is there a way to demonstrate strength of a Hierarchical Bayesian Model versus a non-Hierarchical Bayesian Model on simulated data?
Is there a way to demonstrate strength of a Hierarchical Bayesian Model versus a non-Hierarchical Bayesian Model on simulated data?
I'm ideally looking for a plot that shows that a Hierarchical ...
- 211
1
vote
0
answers
28
views
Nonconvergence of some parameters in MCMC of Hierarchical Bayesian Model
In short:
MCMC is used to construct posterior distributions for parameters of central tendency and all parameters used in the formula for this central tendency. I only care about the parameters of ...
- 41
0
votes
0
answers
41
views
Why don't we typically drop a category as a baseline in Bayesian hierarchical linear regression?
Let's say we have two categorical variables the first with categories $j = 1,..., J$ and the other with categories $k = 1,...,K$. Often in Bayesian hierarchical linear regression, we might have a ...
- 7,884
2
votes
0
answers
45
views
Post-hoc identifiability for Bayesian multilevel regression model
In [1], Ogle & Barber discuss a method for ensuring identifiability of certain Bayesian multilevel regression models; they call this method "post-sweeping". I have a couple of related ...
- 21
0
votes
0
answers
55
views
Statistcially assessing how similar curves are?
I have intensity curves (~9 reps) of bacterial fluorescence over 2.2 cm from 4 groups (A, B, C and D unknown) and three treatments (10 mM, 1 mM and 0 mM). My current code is below. I wish to show how ...
0
votes
0
answers
63
views
Multilevel (Hierarchical) Bayesian Model in R
I have my dataset with different mutations as unit of analysis. These mutations belong to 5 different classes. Also, I have collected, 9 features about these mutations. In other words I have 12 ...
- 1
0
votes
0
answers
14
views
LOOCV comparison partially polled vs unpooled model
When using the leave-one-out cross-validation (LOOCV) as a metric, is the unpooled Bayesian model bound to outperform the partially pooled Bayesian model?
- 33
3
votes
1
answer
62
views
Dropping a hierarchical linear model intercept when centering the outcome at 0?
Suppose a hierarchical linear model with "random intercepts" $\mu_i$ fit to some raw (unscaled) data:
$$y_i \sim N(\mu_0 + \mu_i, \sigma) \\
\mu_i \sim N(0,\sigma)$$
If I rescale $y_i$ by ...
- 731
0
votes
0
answers
21
views
How do I interpret the slope of a random slope model?
I am trying to use a Bayesian random slope model to determine whether the hierarchical structure of the data is biasing my results. I am investigating the effect of IQ on test scores. I have three ...
- 21
0
votes
0
answers
9
views
Method for type S error control with small number of testings?
I have gone through Gelman's paper http://www.stat.columbia.edu/~gelman/research/published/francis8.pdf. It covers a Bayesian testing procedure for hierarchical models.
$Q:$ Is this procedure ...
- 1,365
0
votes
0
answers
32
views
Does marginalizing the covariance of a Normal (with a Wishart prior, not inv-Wishart) lead to a t distribution?
It's known that integrating out $\Lambda \equiv \Sigma^{-1}$ below,
$$ y|\Lambda \sim \mathcal N(0, \Lambda^{-1}), $$
$$ \Lambda \sim \mathcal W(M^{-1}, \nu) $$
leads to a multivariate t distribution ...
- 1,472
0
votes
0
answers
16
views
How to provide data for the "PROX" argument in BayesSAE R-package (To Model the Spatial Fay Herriot SAE)
I am trying to apply Fay Herriot (FH) with Spatial structure (CAR=Conditional Auto Regression) using BayesSAE Package in R (here is the link to the package: https://cran.r-project.org/web/packages/...
