Questions tagged [hierarchical-bayesian]
Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions
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Code help - a mixed model lmer- hierachy level 1 response variable and all Level 2 explanatary variables and an additional crossedrandom effect
I am running a mixed effect model using lmer in lme4.
I was wondering if someone can tell me if this is the correct code to include Fixed effects that are recorded at a different level to the response ...
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1answer
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Modelling strategies for analyzing an effect of a predictor through higher hierarchical level
What strategies can be considered when a predictor's direct effect can not be measured directly due to unmeasured confounding? However, data has a hierarchical structure (patients within regions) that ...
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Defining an LKJ prior not centered at zero
I am working with a Hierarchical Bayesian Model. In each of its units, I need to define a covariance matrix between 2 variables. I am planning to sample the covariance matrix from the LKJ prior. ...
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2answers
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How does one compute the posterior in a two-stage Bayesian model?
Given a random variable $X$ depending on a parameter $\theta$ which itself depends on a parameter $\psi$, how do I compute $p(\theta|X,\psi)$?
A website I have found$^1$ claims that $p(\theta|X,\psi)=...
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How would a Bayesian answer this question from Jeffrey Wooldridge
Jeffrey Wooldridge, a famous econometrician, posed the following question to Bayesians on twitter:
I think frequentists and Bayesians are not yet on the same page, and
it has little to do with ...
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1answer
44 views
What is the difference between Bayesian Regression and Bayesian Networks
I had actually posted an earlier question about the applications of Bayesian networks, and I received a very good response. I understand that Bayesian networks are usually used to answer probability ...
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1answer
38 views
Hierarchical circular-circular regression in R
I have two circular variables and I want to see if they're correlated.
The data comes from a hierarchical and unbalanced experimental design: each participant provided multiple responses and there's ...
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14 views
hierarchical models and m:m/matrix relationships
I have a still rudimentary understanding of hierarchical models so please bare with me. The standard text book example uses a tree/hierarchical structures like this:
...
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Working with lognormal distribution in hierarchical model with JAGS
I am trying to investigate the parameters of a model, that should describe lognormal distributed data. Therefore it should fit to the data in the first place. Hence I want to compare the posterior ...
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To obtain the BPM should the BMA model be worked out?
In section 8.4 of this book: An Introduction to Bayesian Thinking, I learned the Bayesian Model Averaging(BMA) model and the Best Predictive Model(BPM).
The Bayesian Model Averaging Model is obtained ...
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16 views
Posterior Predictive distributions: beta-binomial models
I am trying to do some inference on binomial proportions and I'm having trouble understanding the posterior predictive distribution of my model.
I am concerned that my model isn't learning anything, ...
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INLA Fitting logistic regression using bym or besag smoothing using neighboring spatial points instead of neighboring polygons
Ordinarily, if you want to account for the effect spatial boundaries have on certain variables. You could fit as follows as highlighted in Virgilio Gómez-Rubio's Bayesian inference with INLA article.
<...
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Bayesian estimate of treatment effect for within-subjects and between-subjects design
Let's say I'm running an experiment with an experimental condition and a control condition, where four subjects in total provide two reaction times each. I'm interested in estimating the treatment ...
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32 views
Hierarchical Bayesian model
Consider the hierarchical Bayesian model with $\mu\sim Uniform(-\infty,\infty)$ prior. This is an improper prior, but go
through the calculations setting the density to 1. Derive the Bayes
estimator ...
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1answer
42 views
Why is Cauchy the default prior for both testing and estimation?
Assume that a data set follows a normal distribution and the prior and posterior both have a normal-gamma distribution. When we are performing Bayesian analysis but don't want any subjective choice of ...
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Chaining/combining logistic and linear models
I have a analysis that is looking to predict the total customer value based on a customer's first purchase amount. I am noticing that a set of features predict whether the customer will purchase ever ...
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Modeling the variance of grouping factors in brms
I have data for which I would like to both model the residual variance and the variance of grouping variables in brms. While the former seems straight forward, I'm not sure if I can do the latter.
For ...
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Finding the distributions for Bayesian Hierarchial Modelling
If Bayesian Hierarchial Modelling deals with the equation
$$ p(\alpha,\theta|x) \propto p(x|\theta,\alpha) p(\theta|\alpha) p(\alpha)$$
Where do we get the distributions for $p(x|\theta,\alpha)$ and $...
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1answer
44 views
Multiple testing for Bayesian revenue models
Following this paper from VWO I have implemented the following model for revenue in a subscription business:
The revenue generated by user $i$ is given by:
$$ \alpha_i \leftarrow Bernoulli\left(\...
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When do we need the hyper prior for the Hierarchical model？
Just questions for that when do we need the hyper prior for the hierarchical model?
For example the first layer of the hierarchical model is $m \sim \text{dnorm}(a,b)$.
What is the difference between ...
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Panel Data: (non-)Hierarchical prior modelling is equivalent to (fixed) random effects frequentist model
In Koop's Bayesian Econometrics, the author states that in a panel data model, where the slope is constant, but the intercept is allowed to change with the individuals being studied, if we impose:
...
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1answer
40 views
Other distribution for random effects than Normal
In frequentist statistics, we always assume that the distribution of the random effects is Normal due to the fact that it makes computations more easy. In Bayesian statistics, we can easily change ...
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Can the “true” prior lead to better posterior estimation?
Suppose we know $X_1,\dots, X_n \sim N(\mu,1)$, and $\mu\sim N(1,1)$, so the true prior is $N(1,1)$. Now if we want to compare the true prior with $N(2,1)$, can we say the true prior is better than ...
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Hierarchical Model for ragged/ unbalanced data (in STAN)
(I'm fairly new to Bayesian modelling please forgive me any minor accidents in my questions)
I'm trying to model a data set in STAN, but don't understand why I get large no. divergent transitions.
The ...
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1answer
95 views
Approaching time-to-event prediction as a classification or regression problem?
I am working on a problem where I try to predict the onset of a reaction (of participants), given a set of time-series signals. I know that the event always happened, it is just a matter of question ...
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1answer
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Transforming prior distribution in inference for binomial N parameter
I'm struggling with question 6 in the Exercises to Chapter 3 (page 80) of Bayesian Data Analysis by Andrew Gelman.
http://www.stat.columbia.edu/~gelman/book/BDA3.pdf
We have data Y modeled as ...
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23 views
Is it meaningful for a Bayesian to look at the point estimation of posterior density?
I understand Bayesian look at the quantile. But is it useful to look at the posterior mean and posterior median?
How to explain it in the plain English?
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11 views
How to do the sensitive analysis for the prior?
I understand bayesian people always do the sensitive analysis for the study.
However, I am confused how we set the sensitive analysis.
My question is how we set the parameter's for the sensitive ...
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1answer
30 views
Is it make sense to set the vague prior when your data size is small?
If the data size is small? should we give the noninformative prior(vague prior) to the data set? I think if the data size is small. It is hard for data to tell the whole story.If you do think we can ...
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55 views
Use mean squared error (MSE) for comparing model fits of Bayesian models
I want to use mean squared error (MSE) to assess/copmare the model fit of the Bayesian models. The formula for MSE is
$MSE=\frac{1}{n}\sum^n_i{(y_i-\hat{y}_i)^2}$
I'm not sure how MSE is used for ...
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1answer
35 views
How to set the gamma prior around the MLE estimate?
I have a MLE estimate for the lambda of the possion distribution.
However, the size of my data sets is very small. I choose use the gamma prior in jags. I want to set my prior around the MLE estimate. ...
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1answer
23 views
How to calculate variance of a hierarchical model?
Say that I have X|θ ∼ N(θ, 1) and θ ∼ N(0, 1). I know the mean of X is 0, but how do I calculate its variance? My guess is that its the variance of both normal distributions added together, but I'm ...
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1answer
32 views
Showing that a posterior is Normal given improper prior
I am having difficulty showing the following problem and I suspect it has something to do with my lack of understanding of the question. The question is this:
Suppose we have an improper prior ...
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3answers
395 views
Serial correlation AR(1) model for residuals: how to generalize to irregular times
I am working on a Bayesian serial correlation model for binary and ordinal logistic models (proportional odds model). I am modeling the serial correlation structure on the random effects of the model ...
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Causal modelling: specifying model additively or hierarchically?
Let's assume we would like to examine regional disparities in income. We are NOT interested in country-wide effects. A DAG tells us to adjust for age and education. DAGs do not tell anything about ...
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Can random effects be used in the spatial LGCP package (from JSS paper by Taylor et al. 2015)?
I am reading the excellent statistical software paper found here in this link. The paper is an R implementation of Log-Gaussian Cox processes for spatial point process applications.
Whilst the ...
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How to parametrize a posterior to use it as a prior in Bayesian statistics?
In my problem, I have two sets of parameters, $\theta_1$ and $\theta_2$, and two datasets $d_1,d_2$ that constrain them with a known likelihood function. There is a certain 'hierarchy' in the model: ...
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Implicit for loops in PyMC3 using likelihood of matrices?
I'm confused about (for lack of a better word) "implicit for loops" in PyMC3. You'll note below that I define a 5x5 matrix, k. This matrix represents whether a specific child answers a ...
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1answer
38 views
What is the relationship between knowing physical conditions of a coin toss and the prior distribution?
I am wondering how knowing the initial physical conditions of a coin toss would affect the prior distribution. As far as I know, Bayesians think the parameter as a random variable, the values of which ...
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How to prove equivalence between models, and show that one (Bayesian hierarchical) model is an extension of another?
Is there such a thing as equivalence between statistical models (in my particular case, Bayesian hierarchical models) ? If so, how to prove it ?
Let me explain myself with an example. Consider a ...
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Dirichlet Process vs Hierarchical Dirichlet Process: coupling among transitions on infinite HMM
I'm new to nonparametric Bayesian, and I am reading a paper about beam sampling for the infinite hidden Markov model. In the paper, it is mentioned that since there is no coupling among the ...
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0answers
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Posterior of a Normal distribution
I have a problem obtaining a posterior of a normal multivariate distribution. The problem is as follows: Assuming $ \mathbf{X} \sim N_p (\boldsymbol{\mu}, \boldsymbol{\Sigma}) $, known $\boldsymbol{\...
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Hierarchical model with a mixture of nested and non-nested levels in PyMC3
I’ve recently learnt how to implement an n-level hierarchical model in PyMC3 from this post. In this example, all levels are nested (Global -> Degree -> State -> County). However, I’m trying ...
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0answers
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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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1answer
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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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1answer
88 views
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 ...
