Questions tagged [cholesky-decomposition]

Question 1

I have a dataset from which I need to construct priors from which to draw vectors of correlated but non-identically distributed random samples. For the sake of example, suppose I have $n$ lognormal ...

Question 2

Posting here as I've been tasked with running ACE models for a twins analysis project I'm working on. ACE models refer to a form of structural equation analysis that seeks to to partition phenotypic ...

Question 3

I’m currently working on a VAR model to analyze the impact of expansionary monetary policy on inequality. The inequality measure is Gini and I control for macroeconomics variables such as GDP and ...

Question 4

If the decomposition of a normal matrix is positive definite, and it's clearly also a square matrix, and each decomposition $L$ is square; it seems that one could invert the result fast, but since I'm ...

Question 5

Here is my attempt to show that INDSCAL as a special case of CANDELINC. I am using the following paper as my reference for definitions. Kolda, Tamara G., and Brett W. Bader. "Tensor ...

Question 6

Let $X$ be a random vector with multivariate normal distribution: $X\sim \mathcal{N}(\mu,\Sigma)$. Let $L$ be the Cholesky factorization of $\Sigma$: $\Sigma = LL'$, so that we can write $$X=L X_0 +\...

Question 7

Given a positive semi-definite $n\times n$ matrix $C$ I would like to construct $n$ random variables $X_1,\dots,X_n$ drawn from $n$ fixed distributions such that $\mathrm{corr}(X_i,X_j) = C_{ij}$. I ...

Question 8

I am trying to optimize an objective function $L(\theta)$ in which some parameters that I aim to recover belong to a covariance matrix, $\Sigma$. $\Sigma$ has a unique structure, which includes ones ...

Question 9

As I understand it, the Cholesky decomposition of a Toeplitz matrix can be computed more efficiently by first embedding it in a circulant matrix then using FFT, but I'm having trouble finding any ...

Question 10

I have a computational model that involves having a set of $K$ covariance matrices, $\{\Sigma_1, ..., \Sigma_K\}$ with each $\Sigma_i \in R^{n \times n}$. Storing all these full covariance matrices is ...

Question 11

I am trying to understand the code from pybasicbayes, which defines the following function to sample from an inverse Wishart: ...

Question 12

I am doing an impulse response analysis involving 3 time series A, B, and C in R. Following Lutkepohl approach, I used the log and diff functions to make them stationary. After creating the VAR model, ...

Question 13

I would like to sample from a multivariate Gaussian distribution with covariance matrix $\Sigma - uu^T $, where $u$ is a vector and $\Sigma - uu^T $ is PSD. I have knowledge of a non-Cholesky ...

Question 14

Let $\mathbf{x}\sim N(0,I)$ and $A$ a real-valued square matrix. The spectral decomposition allows us to rewrite a quadratic form $\mathbf{x}^\top A \mathbf{x}$ as a sum of iid chi-squared random ...

Question 15

Given a set of $m$ examples $x$ arranged as rows in $m\times n$ data matrix X, consider Cholesky decomposition of covariance matrix $X'X$. Is there a statistical interpretation of diagonal entries of ...

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Questions tagged [cholesky-decomposition]

Generated correlation random numbers with arbitrary, non-identically distriubuted distributions

Cholesky ACE model (genetics modelling) with ordinal variable

How to shock a VAR Model? Effect of interest rate change on Gini

Does a normal matrix have a "very fast" inverse after doing cholesky?

INDSCAL as a special case of CANDELINC

Cholesky factorization of a conditional multivariate normal distribution

Sampling with specified covariance matrix and distribution

Passing a cholesky decomposition for a matrix with constrained variances to an objective function

Fast Cholesky decomposition of a Toepllitz matrix via embedding in a circulant & fft

Efficient way to encode a set of large covariance matrices

How to sample efficiently from an inverse Wishart distribution?

Interpretation of impulse response analysis - Cholesky decomposition output in R

General matrix decomposition downgrading algorithm for sampling

Spectral decomposition and quadratic forms

Statistical interpretation of diagonal of Cholesky decomposition?

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