# Questions tagged [wishart]

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

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### Proper metric for the distance between two Wishart distributions

Let $A$ and $B$ be samples acquired from two distinct Wishart distributions $X$ and $Y$, respectively. The sampling units in $A$ and $B$ are two distinct sets of $p \times p$ random matrices. I want ...
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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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### 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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### The multivariate normal distribution has the same relationship with the Wishart distribution as the multivariate t-distribution with the …?

Is there a name for the distribution resulting from the sum of outer products of t-distributed random vectors? Alternatively, is there a matrix-valued distribution with the support of positive ...
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### Informative prior for Normal-Inverse Wishart distribution

In Bayesian analysis we use the Normal-Inverse Wishart distribution for the parameters of multivariate models these prior distributions have some hyperparameters. So how do we find the values of ...
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### Prior distribution importance in Bayesian inference

I am performing a Bayesian multivariate regression, and therefore I have to construct the prior and the subsequent posterior. But the paper that I am using as a reference, uses a "Uninformative prior"...
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### Can Wishart be close to Normal distribution?

I'm trying to figure out if Wishart can be close to Normal for a number of degrees of freedom enough large. About chi-squared distribution, Wikipedia states: ...
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I have been struggling computing the Fisher's information of the Wishart distribution. I'll write what I have gone through. Let's $\Omega$ denote a $p\times p$ Wishart random variate denoted by $\... 0answers 43 views ### Eigenvalue order of magnitude for Wishart random matrix If we have a$P\times N$matrix$\mathbf{A}$whose elements$A_i$are samples (in this case, P samples) from a multivariate gaussian distribution in an$N$dimensional space, we can define the Wishart ... 0answers 237 views ### Simulating from an Inverse Wishart with constraints Let$\Sigma$be a$p\times p$positive definite matrix and$\nu>p-1$. I would like to simulate a realization of the Inverse-Wishart distribution$X\sim\mathcal W^{-1}(\Sigma, \nu)$with the ... 0answers 34 views ### How to find the distribution of$B*=BSB^T$, where$S$is the sample covariance from normal observations? Let$X_1, X_2, \dots, X_{30}$be a random sample of size$n=30$from a$N_5(μ, Σ)$population. If B is a$2\times 5$matrix $$B = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 \\ 1 & 0 & ... 0answers 200 views ### Log Expectation of Inflated Determinant of Wishart Distribution Let \Lambda \sim \mathcal W(\nu, \Psi), i.e., following a n \times n dimensional Wishart distribution with mean \nu \Psi and degrees of freedom \nu. The expectation of the log determinant of \... 1answer 88 views ### Simulation under Wishart-like constraint in \mathbb{R}^{k\times p} Given a (p,p) symmetric positive semi-definite matrix \mathbf{H} of rank k\le p, I am looking for a (possibly efficient) way of generating a set of k vectors \alpha_i\in\mathbb{R}^p ... 1answer 372 views ### Covariance Matrix Eigenvalue Distribution Relation to Size [closed] I'm trying to run PCA on sample covariance matrices of various sizes (ranging between 20 x 20 to 4000 x 4000). Assume the data follows a joint multivariate normal distribution. While derivations are ... 0answers 353 views ### Intuitive explanation for Marchenko-Pastur law I am looking for an intuitive reasoning behind the Marchenko Pastur law, which is described as a law of large numbers analog for random matrices. I know the law gives the probability density function ... 0answers 132 views ### Posterior pointwise uncertainty of multivariate normal-Wishart (variational GMM) Given a variational mixture of Gaussians (as per, e.g., Chapter 10 of Bishop, 2006), we can compute the posterior predictive pdf:$$ \left\langle p(x|\alpha,\beta,\nu,\mu,V) \right\rangle$$where$\...
If $\mathbf{M} \sim W_2(\Sigma, 3)$ is a Wishart matrix and $\Sigma =\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$ then what is the distribution of $(3, 1) \mathbf{M}^{-1}(3,1)^T$ ? Thank ...