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Questions tagged [cholesky]

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1answer
21 views

Conserve correlation with simulate data

let me explain you the process, I have random variables in a matrix $X_1$: $260\times3$. I have my correlation matrix $\rho_1$: $3\times3$ from my matrix $X_1$. Now I use a Cholesky decomposition ...
3
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0answers
338 views

Constructing a positive definite covariance matrix

I am trying to construct a covariance matrix between a set of demands $t \in T$. The only information I have of the demands are the mean and the standard deviation. I intend to apply Cholesky ...
3
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0answers
87 views

Mahalanobis distance for highly multivariate random variable

I have to compute the Mahalanobis distance for a $10^6$ dimensional multivariate random variable. What is the best (and fastest) way to do this? I am currently taking cholesky decomposition of the ...
3
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0answers
179 views

effects of Box-Cox transformation on covariance

I'm trying to synthesize data for a Monte Carlo simulation. I have a stationary random process $x$ and can readily estimate its covariance matrix $S$. I know that if the increments of the process are ...
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0answers
26 views

Eigenvalue decomposition of a covariance matrix using a fast Cholesky decomposition

Let $\mathbf{C}$ be a $n \times n$ covariance matrix and assume that the LDL' Cholesky decomposition can be obtained efficiently. Can we take advantage of this to obtain a fast eigenvalue ...
2
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0answers
31 views

Cholesky Decomposition (in lmer from lme4)

When I retrace the implementation of lmer from lme4 I faced a question regarding cholesky decomposition used for solving penalized least squares. Consider a Cholesky decomposition of a matrix M with ...
2
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0answers
340 views

IRF function with several exogenous covarites (SVAR model)

How to interpret an IRF function with exogenous covariates. Example: Small open economy which I control for foreign variables (Endogenous variables cannot influence the exogenous variables). The ...
2
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0answers
123 views

Uncorrelating correlated $\chi^2$ distribution

This question is related to my previous question in here So I was trying to simulate correlated $\chi^2(1)$ random variables given the desired co-variance matrix. However, it seems like the only ...
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0answers
41 views

A transformation from uniform random variable to Gaussian mixture

I am attempting to describe a prior_transform for a multivariate Gaussian mixture in order to estimate the evidence integral of that prior convolved with another likelihood distribution. This is ...
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0answers
231 views

Can someone provide a non-technical explanation of how Cholesky Covariance priors work?

I am looking for an explanation of how Cholesky Covariance priors work in the context of mixed effects regression. In particular, when they are applied to the correlations among random effects. What ...
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0answers
81 views

Simulating data with local correlations

Im writing my thesis, which a monte-carlo study aimed at generating datasets for comparing the performance of various regression models (Neural networks amongst others). And since neural networks can ...
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0answers
72 views

Sequential conditional simulation to avoid using a large covariance matrix

I would like to generate $S$ samples of a $T \cdot M$ dimensional vector, where $T$ is the number of time steps and $M$ the number of locations, i.e., the vector is a stack with $T$ values for ...
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0answers
160 views

Decomposition of a random vector into uncorrelated components

I have a set of random vectors $Y_i$ and their correlation matrix $C_{i,j}$. Each vector can be thought of as a sum of two uncorrelated vectors $Y_i=A_iX+B_iY$, where $X,Y$ are the same vectors for ...
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0answers
632 views

Trying to use Cholesky decomposition of covariance matrix to sample error ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. In a previous question when I asked about this (...
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0answers
13 views

Cholesky decomposition in control variates method (Monte Carlo variance reduction technique)

The control variates method, used as a variance reduction technique for Monte Carlo simulations, takes one new variable $t$, correlated to the random variable $m$ to estimate (using the same notations ...
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0answers
64 views

Generalized linear regression with custom variance-covariance matrix in R

I want to compute the estimate of $\beta$ for a linear model $Y = X\beta + \varepsilon $ with $$\varepsilon \sim N_d(0, \sigma^2V),$$ where $V$ is a $d\times d$ definitive posive, symmetric matrix. ...
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0answers
756 views

Cholesky decomposition of the covariance matrix: not positive definite?

I am implementing a multivariate simulation in R and when applying the Cholesky decomposition to the covariance matrix I get: the leading minor of order one is not positive definite How could the ...
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0answers
115 views

DCC GARCH and cholesky factorization

I want to run a simulation experiment after I have estimated my DCC GARCH parameters (following Becker et al. methodology) Basically, since I am rather unfamiliar with the application of cholesky ...
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0answers
27 views

Create iid normal random vectors

Le us create N independent and identitcally distributed (iid) normal random vectors with zero mean and specific covariance matrix. Each vector is of size p. Let $\Sigma$ be the specific covariance ...
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0answers
53 views

Evaluate the multivariate normal using variance matrices $\boldsymbol{\Lambda}+\alpha_{i}\mathbf{a}\mathbf{a}^{T}+\beta_{j}\mathbf{b}\mathbf{b}^{T}$

I need to calculate a huge amount of inverses and determinants to evaluate the pdf of the multivariate Gaussian. Specifically I need to compute the inverses and determinants of the following ...