Questions tagged [hierarchical-bayesian]
Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions
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Confused on Bayesian Decision Theory
I am trying to understand what is the right way to pick up an "action", as it is called in Murphy, Machine Learning a Probabilistic Perspective, in the 'chatper 'Bayesian decision theory'.
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two-step gibbs sampling vs block gibbs sampling
While reading Bayesian-related technical articles, I can see algorithms such as two-step Gibbs sampling and block gibbs sampling ...
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What is the difference between hierarchical modeling and setting a (fixed) prior on a parameter?
I was reading through Chapter 11 of Data Analysis using Regression & Multilevel Models, and was confused by a slight variation of a simple hierarchical model posed in the text.
Lets say I have a ...
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For a separable covariance in a Gaussian process, is an inverse Wishart prior conjugate?
Suppose we have a GP for the vector $\mathbf{y}\sim\text{GP}(\boldsymbol{0},\Sigma_y)$, where $\Sigma_y=\Sigma_r\otimes\Sigma_f$ is a separable covariance matrix. Assume $\Sigma_f$ is fixed and an ...
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Hierarchical models and conditional independence
Suppose that we have a hierarchical model given by (this is Example 4.4.5 of Berger and Casella(2002))
\begin{align*}
X\mid Y&\sim\text{binomial}(Y,p),\\
Y\mid\Lambda&\sim\text{Poisson}(\...
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Conditional independence in BUGs/JAGs?
I am trying to create a hierarchical model in BUGs. I am actually attempting to implement this is Nimble, but I suspect that a JAGs implementation will be informative.
To attempt to reduce my problem ...
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Sequential updating vs Marginalized updating
Suppose I need to sample a posterior $\pi(\theta|D)$, whose analytic form is not tractable (not even up to a normalizing constant). However, I somehow manage to obtain an augmented posterior $\pi(\...
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Independent statements in model definition and then DAG
In this paper in Section 3.1, they give a Baysian linear regression model and then a DAG, which I show below.
From my understanding a DAG tells us how the joint distribution can be factorised.
But in ...
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Bayesian network extracting further conditional independence statements then just from d-separation theorem
Given a Bayesian network $(p,\mathcal{G})$, where $p$ is our joint distribution, and $\mathcal{G}$ is a DAG.
Then by the d-separation theorem we can deduce conditional independence statements, in ...
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How to decompose the conditional posterior prob? [closed]
I am learning bayesian inference now. A problem I encountered a lot of time is, when I need to calculate or simplify the posterior prob., I don't know how should I begin, according to what I have.
For ...
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Using PCA to check if parameters simulated from a hierarchical Bayesian model are close to real parameters
I have a hierarchical Bayesian model that learns a 5-parameter function for each of the N participants. The priors on each of the 5 parameters are parameterized by a scale parameter, so, it also ...
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Proposal parameterization accuracy for Importance Sampling
Suppose I am fitting a Bayesian mixture model that's structured as follows:
$$
Y_i | (z_i = k) \sim \mathcal{N}(\mu_k, \sigma_k^2), \quad k = 1, \cdots, K
$$
$$
z_i \sim \text{Mult}(1; w_{i1}, \cdots, ...
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E(X1 | X2 > X3) for (X1,X2,X3) multivariate normal
I'd like a closed form solution for $E(X_1 \mid X_2 > X_3)$ where $(X_1, X_2, X_3)$ is multivariate normal with possibly arbitrary mean vector and covariance matrix.
The conditional distribution $f(...
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Zero inflated and right skewed dependent variable – is the Tweedie distribution a good solution?
We are conducting a variance decomposition using a hierarchical linear random effects Bayesian model to investigate the variance in a DV that is affected by three nested layers. Because the DV is ...
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Width of Confidence Intervals for Variance Estimates in Contrast to Point Estimates
We are conducting a variance decomposition using a hierarchical linear random effects Bayesian model to investigate the variance in a DV that is affected by three nested layers. We estimate credible (...