# Questions tagged [cholesky-decomposition]

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### A new method for processing music scores?

I have developed a method and python script: https://github.com/githubuser1983/algorithmic_python_music which allows the user to input a midi file and then chose a few numbers as parameters, and the ...
208 views

### How do I generate $n$ random variables that follow a correlation matrix with individually log normal distributions?

Short and sweet: I'd like to model $n$ random variables representing price changes of individual assets. Each of these should be distributed as a log normal variable with a median of 1. Is there a way ...
• 190
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### Does the Cholesky decomposition of a covariance matrix lead to a lower triangular matrix with positive diagonals?

We know that an $N\times N$ covariance matrix $\Sigma$ is symmetric positive definite, and can be factorized using Cholesky decomposition as follows $$\Sigma=LL'$$ where $L$...
• 1,030
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### Homework - Gaussian Process with Cholesky Decomposition

For b), I have: But I can't seem to fit the "facts" given in the problem anywhere. What am I missing here? Any help/hint is appreciated!
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### Drawing samples from matrix normal

I have to generate $n \times m$ sample ($A$) from a matrix normal distribution, given two covariance matrices: $n \times n$ row covariance matrix (matrix $B$) (defines the covariance between the rows ...
• 51
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### Cholesky decomposition lower triangular in Gaussian process sampling

I am trying to intuitively understand the Cholesky decomposition in gaussian process function sampling. I understand it as as the square root of the covariance matrix being the multivariate ...
• 619
1 vote
63 views

### Proof that variance-covariance matrix of var(b|X) - var(b*|X) is positive-semidefinite [closed]

I'm having trouble finding the proof to show that the variance-covariance matrix of var (b|X) - var (b*|X) is positive-semidefinite. OLS estimator = GLS estimator = Hint: Note that A is the Cholesky ...
• 11
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### Relationship between Cholesky decomposition and matrix inversion?

I've been reviewing Gaussian Processes and, from what I can tell, there's some debate whether the "covariance matrix" (returned by the kernel), which needs to be inverted, should be done so ...
• 1,650
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### How to Incorporate Skew Into Simulated Data?

Suppose I have a dataset $\mathbf{X}$ which is a $n \times m$ matrix of $n$ independent realizations of some $m$-dimensional random vector $\mathbf{x}$. I want to generate a new dataset $\mathbf{X}'$ ...
• 2,777
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### Betareg error when running bootstrap-like simulations (Error in chol.default(K) : the leading minor of order 16 is not positive definite

A previous post discussed a similar case on non-positive definite covariance matrices resulting when producing half-normal residual plots using the package betareg. However, I would like additional ...
89 views

### Getting sets of random correlated variables

For the training of a machine learning model I need to add additional features, and these features are correlated. I need to run the model N times adding these features with random values, and for ...
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