Questions tagged [cholesky]

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55 questions
24k views

How to use the Cholesky decomposition, or an alternative, for correlated data simulation

I use Cholesky decomposition to simulate correlated random variables given a correlation matrix. The thing is, the result never reproduces the correlation structure as it is given. Here is a small ...
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Residual sum of squares of block matrix with sparse elements

Based on the question Residual Sum of squares in Weighted regression, a fast way to solve for $$(\mathbf{y-X\hat{\boldsymbol\beta}})^{'}\mathbf{C}^{-1}(\mathbf{y-X\hat{\boldsymbol\beta}})$$ is to ...
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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 ...
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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 ...
364 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 ...
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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 ...
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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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Simulate Moderated Regression with Cholesky Decomposition

I want to simulate a moderated regression where the slopes are standardized (i.e., can be interpreted like correlations), and I am wondering how to do this with Cholesky decomposition. My initial ...
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R: difference between Generalized Least Square and the Standard Least Squares with Cholesky

According to Wikipedia (source of all truth and knowledge...), http://en.wikipedia.org/wiki/Generalized_least_squares#Properties a weighted least square regression is equivalent to a standard least ...
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Relation of kernels and Cholesky decomposition

I am trying to find an intuition on why we require that kernels are positive semi definite and I have found this: We are given a dataset $X$ of size $n \times d$ where $n$ is the number of samples ...
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Choleski decomposition of the covariance matrix

I have a process described as $r_t = \mu + \Sigma_t^{1/2}z_t$ where $z_t$ is let's say a standard normal distribution residual and $\Sigma_t$ is the conditional covariance matrix. The $t$ stands ...
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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 ...
276 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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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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numpy.linalg.cholesky of correlation matrix with small eigenvalue gives error [duplicate]

When doing a Cholesky decomposition of a covariance matrix with very low eigenvalues, numpy.linalg.cholesky and ...
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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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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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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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How to find unknown correlation coefficients in a correlation matrix from known correlation coefficients? [duplicate]

I have a correlation matrix A given below. Here A should be a positive-definite matrix so that we can perform Cholesky decomposition of A. ...
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Estimating correlation matrix using numeric likelihood maximization

I'm performing maximum likelihood estimation on jointly distributed data and I'm having some issues estimating the correlation terms. I am using an approach based on the Cholesky decomposition, but I ...
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Are VAR and VEC models theoretically neutral?

I have recently been introduced to Vector Autoregression (VAR) and Vector Error Correction (VEC) models in an Econometrics class, where both approaches were presented as a neutral way to test economic ...
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Cholesky Shock - Interpretation of logs in IRF Models

I came across a few articles here and there that conclude: When the data (say variables X, Y) for an impulse response function are on log level, the y-axis depicts the % response of Y to a 1% shock ...