# Questions tagged [hierarchical-bayesian]

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

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### Bayesian Model(Write out likelihood and prior)

I am working with a dataset regarding transmission rate for a disease spreading among cattle at different farms during a 5-month period. The goal is to estimate the transmission parameter $\alpha$ ...
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### Is stationarity of variables neccessary condition for Bayesian VAR?

I am trying to run a BVAR on 5 variables. Four out of five are non-stationary. So shall I do the first difference of the non-stationarity variables or take them in level for running the BVAR? And what ...
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### Estimating the likelihood of a Dirichlet process

I am not sure if what I'm trying to achieve makes sense or is even possible, but I'd like to do MLE on a Dirichlet process mixture model. My reasoning is the following: If we can write out the ...
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### Hierachical model causing too much shrinkage?

I use population-wide, 12-year data for examining regional differences in rehabilitation use (zero-inflated, lognormally-distributed outcome variable). I analysed the outcome variable with 2 models: <...
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1 vote
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### Parallel with Weighted Least Squared in Bayesian Regression

I have a dataset with a column of ratios $Y = z_1 / z_2$, which will be my depending variable, and a set of columns that explain $Y$. Here $z_1$ means "imports" and $z_2$ means "exports&...
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### Bayesian estimation under transformation on the paramater

Consider the classical model Normal-Normal-Inserse-Gamma model: $$x=(x_1,...,x_n)|\mu,\sigma^2\sim N(\mu,\sigma^2)\,\,(iid),\,\,\mu\sim N(m_0,\tau),\sigma^2\sim IG(a,b),$$ where $m_0,\tau,a,b$ are ...
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### Samples from Conditional Posterior Distribution in Pymc3

Let us consider the following Hierarchical Bayesian model: $w \sim\ Beta(20, 20)$ $K = 6$ $a = w * (K - 2) + 1$ $b = (1 - w) * (K - 2) + 1$ $theta \sim\ Beta(a, b)$ $y \sim\ Bern(theta)$ The above ...
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### Is it possible for a hierarchical model to forecast a sub-region with complete lack of data as "borrowing strength"?

I am looking at sales time-series data (weekly from Jan to Dec 2021) which has a natural hierarchical structure by geography. For example, storeA1, storeA2, .... storeA99 located in Neighborhood A, ...
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1 vote
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### Using Pairwise Differences Between Two Conditions as Data (Bayesian)?

Suppose I have measurements for the expression-level of a "gene" from two groups of arbitrary (possibly different) sizes. Maybe one group is a control and the other treated. $x$ = <4.5, 5....
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### Data-informed grouping of covariates in Bayesian Hierarchical Modeling?

Is there a way to place a prior on the first stage's betas that allows the second stage groups to be determined from the data? I am working with co-exposures where I am not super confident in how they ...
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### Why is my proportion estimate 0? (BEST MCMC Bayesian inference)

I am trying to run a simple Bayesian inference on my y1 vector as shown below. ...
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### How to improve model accuracy fitted by extreme skewness distribution in brm()

I first fit a bayesian model by brm() in R. Because I’m not very familiar with Bayesian frameworks, I didn't specify priors distribution. My data ranges from -1~12 ...
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### One-step prediction in JAGS of a dynamic model with unknown variance

I have the following problem. I have a linear dynamic model as follows: $$\theta_{0}\sim N(0,10)$$ $$v,w\sim \text{InverseGamma}(0.1,0.1)$$ \theta_{t}\sim N(\theta_{t-1},w), \hspace{0.3cm} y_{t}\sim ...
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### Interaction term to hierarchical model

Assume we have a response variable of interest Y and a predictor of interest X1, that might be associated with another predictor X2, and we do a linear regression with interactions: Y = B0 + B1X1 + ...
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### Conjugate Hyperpriors

I heard it was possible to have a Bayesian model with likelihood, prior and hyperprior that has a posterior of closed form, by choosing a conjugate prior and conjugate hyperprior. But I struggle to ...
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### Bayesian hierarchical model inference problem image segmentation

it might be really confusing question. I am working on my thesis and I am stuck at a problem. It's a problem in image segmentation and finding parameters of border lines of continuous region in an ...
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### Using Hierarchical Gaussian Linear Regression to Inference of a Breakpoint Position

Edit: this question is not a duplicate of imposing a perpendicularity constraint in Gaussian linear regression. Here, the question is about hierarchical reference of the breakpoint position. The other ...
1 vote
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### Modeling with Negative Probabilities?

Background: As I understand the role of probability in Quantum Mechanics, the idea is that no observable event can have negative probability, but that it can make sense for unobserved quantities to ...
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