(This article was originally published at R – Xi'an's Og, and syndicated at StatsBlogs.)
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.
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Scott Lynch 
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Tags: Bayesian Analysis, books, correlation, cross validated, introductory textbooks, Kids, Linear algebra, positive definite matrix, R, Scott Lynch, statistics, University life
