Questions tagged [hierarchical-bayesian]

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

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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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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
37 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
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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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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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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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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
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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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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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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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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
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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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367 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
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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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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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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
66 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 ...
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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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1answer
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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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1answer
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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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45 views

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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1answer
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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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1answer
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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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