# Questions tagged [cholesky]

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### 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 ...
184 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 ...
55 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 ...
44 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 ...
369 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 ...
352 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 ...
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 ...
46 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 ...
297 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 ...
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 ...
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 ...
167 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 ...
641 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 (...
22 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 $\mathbf{X}'$ ...
79 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 ...