The wishart tag has no wiki summary.
7
votes
1answer
52 views
Generate covariance matrix with fixed values in certain cells
I want to be able to generate a covariance matrix of dimensions $D$ x $D$, such that certain specified cells of this matrix contain a fixed predetermined values (at least approximately).
For e.g. For ...
0
votes
1answer
59 views
Degrees of freedom for Gaussian Process
I am reading this paper on Generalised Wishart Process (GWP). It is about modelling covariance matrix of D - dimensional gaussian processes (GP) as GWP. I fail to understand interpretation of "degrees ...
6
votes
1answer
173 views
Covariance matrix for Gaussian Process and Wishart distribution
I'm reading through this paper on Generalised Wishart Processes (GWP). The paper calculates the covariances between different random variables (following Gaussian Process) using squared exponential ...
4
votes
0answers
84 views
Joint distribution of two distances
Suppose there are three points in 3D space, each with coordinates $A_i=(X_i,Y_i,Z_i)\leadsto \mathcal{N}(\mu_i,\tau^2\mathbb{I}_3)$. We compute the distance between the three points, e.g. $D_{ij} = ...
5
votes
1answer
310 views
Hyperprior distributions for the parameters (scale matrix and degrees of freedom) of a wishart prior to an inverse covariance matrix
I'm estimating several inverse covariance matrices of a set of measurements across different subpopulations using an wishart prior in jags/rjags/R.
Instead of specifying a scale matrix and degrees ...
6
votes
1answer
207 views
Expected value of the log-determinant of a Wishart matrix
Let $\Lambda \sim \mathcal W_D(\nu, \Psi)$, i.e. distributed according to a $D \times D$ dimensional Wishart distribution with mean $\nu \Psi$ and degrees of freedom $\nu$. I would like an expression ...
3
votes
0answers
173 views
Distribution of a normalized inverse Wishart times Gaussian
Suppose $z\sim\mathcal{N}\left(\lambda^2 e_1,I_n\right)$ where $e_1$ is the first column of the $n$-dimensional identity matrix, denoted here as $I_n$. Suppose $S\sim\mathcal{W}\left(m,I_n\right)$ is ...
6
votes
0answers
194 views
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 ...
3
votes
0answers
226 views
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 ...
1
vote
1answer
493 views
How to sample from a Wishart distribution?
From Wikipedia, we know that $n$, the degrees of freedom, should be larger than $p-1$ where $p$ is the dimension of the scale matrix.
Also, from the bottom part of the same article, we see "Bartlett ...
1
vote
0answers
202 views
Generating correlation matrices using Wishart distribution
I have problem on generating correlation matrices using Wishart distribution. I read some articles about Wishart distribution, and it turns out that Wishart distribution is commonly used to generate ...
2
votes
2answers
188 views
What is the distribution of norm induced by an inverse Wishart?
Suppose $S$ is distributed as a Wishart matrix with $n$ degrees of freedom and scale matrix $\Sigma$, and let $\vec{a}$ be a fixed vector. It is well known that $\vec{a}^{\top}S\vec{a}$ is equal to
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