# Questions tagged [wishart]

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

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### Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...
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### Entropy of Inverse-Wishart distribution

What is the entropy of the Inverse-Wishart distribution? I need just a reference, but derivation (e.g. using inverse property) would be interesting too.
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### 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 ...
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### Sampling distribution of average of some covariance matrices

I have $K$ datasets, each with $N$ variables and $M$ samples (they are in fact EEG time series, but I discard time and treat them as $K$ iid multivariate samples) and assume they are coming from the ...
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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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### 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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### 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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### 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 ...
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I have a problem deriving two expectation involving Wishart distributions with mean zero. Let $\bf{W} \sim {W_p}({\bf{\Sigma }},$$n\bf{)} and \bf{A}$$: p\times q$. Prove that $E[\bf{A(A'WA)^-A'W}]... 0answers 159 views ### Question on Inverse-Wishart Distribution when reading Peter Hoff's book I have a couple of questions when reading the chapter 7 The Multivariate Normal Model of Peter Hoff's "A First Course in Bayesian Statistical Methods". First, could anyone give me any resource about "... 0answers 773 views ### Sample from Wishart distribution with inverse Scale matrix I tried to model precision matrix in a hierarchical Bayesian setup with Wishart prior given d.f. and inverse scale matrix, and matrix normal likelihood, since it's a conjugate prior, my posterior on ... 0answers 19 views ### How to simulate coefficients from a multivariate distribution and the variance matrix from a inverse Wishart distribution? I have estimated a Seemingly Unrelated Regression (SUR) and I would like to simulate the coefficients using the posterior distribution. When researching how to do that, I have read that you should not ... 0answers 28 views ### Kullback–Leibler divergence between two inverse Wishart distributions Is there a closed form formula for the KL divergence between two inverse Wishart distributions? 0answers 40 views ### How to Estimate Covariance Matrix using Wishart Distribution? I learned that Wishart distribution can help estimate covariance matrix of MVN without sampling directly from MVN. But there are some points that are still unclear for me: Why we bother to estimate ... 0answers 25 views ### Proper metric for the distance between two Wishart distributions Let$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$random matrices. I want ... 0answers 220 views ### Expectation of the inverse of$\textbf{z} \textbf{z}^{H}$where$\textbf{z}$is a complex Gaussian vector Considering the vector$\textbf{z} \sim \mathcal{CN}(\textbf{0}_{M},\Theta_{M \times M})$, what would be the expectation of$\frac{1}{\textbf{z} \textbf{z}^{H}}$, i.e.,$\mathbb{E} \left\lbrace \frac{...
I am solving the next exercise about a property of a Wishart Distribution: $$M_1\sim W_p(\Sigma,n_1)$$ $$M_2\sim W_p(\Sigma,n_2)$$ are independent, then $M_1+M_2\sim W_p(\Sigma,n_1+n_2)$ I have ...