# Questions tagged [wishart-distribution]

The Wishart distribution is a common matrix distribution on square symmetric semi-definite matrices.

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### Clustering with gaussian mixtures: choice of hyperparameters

Question: I am interest in general in understanding how to choose the hyperparameters if we are interested in clustering bivariate vectors assuming a mixture of Gaussian mixture with conjugate Normal-...
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### Is there a closed form solution for the Hellinger Distance between two Wishart distributions?

Given two Wishart distributions $X_0 \sim W_{p_0}(V_0,n_0)$, $X_1 \sim W_{p_1}(V_1,n_1)$, what is the Hellinger Distance between them? Can it be obtained in closed form assuming $p_0 = p_1$? For ...
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### Marginal likelihood of bivariate Gaussian model

I assume the following model for a sample $y_1 \in \mathbb{R}^2$ of size $1$ with bivariate Gaussian likelihood and independent bivariate Gaussian and inverse-Wishart prior for the mean and variance ...
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### How to simulate coefficients from a multivariate distribution and the variance matrix from a inverse Wishart distribution?

I have estimated a Seemingly Unrelated Regression (SUR) and I would like to simulate the coefficients using the posterior distribution. When researching how to do that, I have read that you should not ...
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### Kullback–Leibler divergence between two inverse Wishart distributions

Is there a closed form formula for the KL divergence between two inverse Wishart distributions?
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### Marginal distribution for the off-diagonal elements of a Matrix following an Inverse-Wishart

I've found on CV the marginal distribution for the main-diagonal elements of a matrix which follows an Inverse-Wishart distribution. However, what will happen to the off-diagonal elements? what ...
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### How to Estimate Covariance Matrix using Wishart Distribution?

I learned that Wishart distribution can help estimate covariance matrix of MVN without sampling directly from MVN. But there are some points that are still unclear for me: Why we bother to estimate ...
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### Is assigning an inverse-Wishart distribution to a diagonal matrix problematic?

I'm reading the paper Bayesian Vector Autoregressions by Thomas Wozniak. He considers the model $$y_t = \mu + A_1 y_{t-1} + \cdots A_k y_{t-k} + u_t$$ where each $y_i$ is a $N$-vector, each $A_j$ is a ...
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### Integrating the inverse-Wishart density

It is alleged in this question and in the Wikipedia article and elsewhere that the density function for the inverse-Wishart distribution with $n$ degrees of freedom on $p\times p$ positive-definite ...
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### What's the role of the scale matrix for the Inverse-Wishart and Wishart distributions?

What's the role of the scale matrix for the Inverse-Wishart and Wishart distributions? The purpose of finding this information is to enlighten me on how should one decide on a prior for a positive-...
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### Expected eigenvalues of a Wishart Matrix

I consider a $n\times n$ Wishart Matrix with expected value $p \cdot I_n$, i.e. a matrix of the form $$W = XX'$$ with $X$ a $n\times p$ matrix with independent standard normal entries. It is easy ...
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### use inverse Wishart for variance in MCMC

When you have a posterior that looks like as one step in Gibber Sampler $P(\xi | \Sigma_\xi, \theta) ∝ exp\{-1/2 \xi\Sigma_\xi^{-1}\xi\}P(data | \xi, \theta)$ Do you always assume inverse Wishart ...
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