Archive for linear algebra

another wrong entry

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , on June 27, 2016 by xi'an

Quite a coincidence! I just came across another bug in Lynch’s (2007) book, Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. Already discussed here and on X validated. While working with one participant to the post-ISBA softshop, we were looking for efficient approaches to simulating correlation matrices and came [by Google] across the above R code associated with a 3×3 correlation matrix, which misses the additional constraint that the determinant must be positive. As shown e.g. by the example

> eigen(matrix(c(1,-.8,.7,-.8,1,.6,.7,.6,1),ncol=3))
$values
[1] 1.8169834 1.5861960 -0.4031794

having all correlations between -1 and 1 is not enough. Just. Not. Enough.

What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix?

Posted in Books, pictures, Statistics, University life with tags , , , , , , on March 30, 2012 by xi'an

This is the question I posted this morning on StackOverflow, following an exchange two days ago with a user who could not see why the linear transform of a log-normal vector X,

Y = μ + Σ X

could lead to negative components in Y…. After searching a little while, I could not think of a joint distribution on the positive k-dimensional quadrant where I could specify the covariance matrix in advance. Except for a pedestrian construction of (x1,x2) where x1 would be an arbitrary Gamma variate [with a given variance] and x2 conditional on x1 would be a Gamma variate with parameters specified by the covariance matrix. Which does not extend nicely to larger dimensions.