# Questions tagged [cholesky]

The tag has no usage guidance.

58 questions
Filter by
Sorted by
Tagged with
5answers
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 ...
3answers
6k views

1answer
237 views

### 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 ...
0answers
67 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 ...
0answers
47 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 ...
0answers
373 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 ...
0answers
360 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 ...
0answers
124 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 ...
1answer
372 views

### 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 ...
1answer
647 views

### 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 ...
1answer
355 views

### 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 ...
1answer
330 views

### 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 ...
0answers
48 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 ...
0answers
329 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 ...
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 ...
0answers
106 views

### 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 ...
0answers
74 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 ...
0answers
168 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 ...
0answers
645 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 (...
1answer
540 views

### 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. ...
2answers
207 views

### 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 ...
1answer
552 views

### 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 ...
1answer
588 views

### 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 ...
0answers
12 views

### Showing a useful result for Wisharts and Multivariate Beta random matrices

Let $\mathbf{A} \sim \text{Wishart}_m\left(k_a,\mathbf{V} \right)$ and $\mathbf{B} \sim \text{Wishart}_m\left(k_b,\mathbf{V} \right)$ be two full rank Wishart random matrices. Define  \mathbf{S} = \...
0answers
23 views

### 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 $\mathbf{X}'$ ...
0answers
82 views

### 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 ...
0answers
61 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 ...
0answers
37 views

### Add Noise to a Dataset

I've generated a dataset of 100 elements from a 3-variate Gaussian distribution with parameters $\mu = 0$ and \$\Sigma = \begin{pmatrix}1 & \rho_1 & \rho_2 \\ \rho_1 & 1 & \rho_1 \\ \...