http://statsathome.com/tags/sampling/ Recent content in Sampling on Statistics @ Home Hugo -- gohugo.io en-EN stats.at.home@gmail.com (Justin and Rachel Silverman) stats.at.home@gmail.com (Justin and Rachel Silverman) (c) 2017 Justin and Rachel Silverman Sat, 27 Oct 2018 00:00:00 +0000 http://statsathome.com/2018/10/27/sampling-from-the-singular-normal/ Sat, 27 Oct 2018 00:00:00 +0000 stats.at.home@gmail.com (Justin and Rachel Silverman) http://statsathome.com/2018/10/27/sampling-from-the-singular-normal/ Following up the previous post on sampling from the multivariate normal, I decided to describe in more detail the situation where the covariance matrix or precision matrix is singular (e.g., it is not positive definite). A normal distribution with such a singular covariance/precision matrix is referred to as a singular normal distribution. Here is 100 samples from a two dimensional example: Notice that a singular normal essentially has less dimensions (in this case 1 dimension) than the dimension of the random variable (in this case 2 dimensions). http://statsathome.com/2018/10/19/sampling-from-multivariate-normal-precision-and-covariance-parameterizations/ Fri, 19 Oct 2018 00:00:00 +0000 stats.at.home@gmail.com (Justin and Rachel Silverman) http://statsathome.com/2018/10/19/sampling-from-multivariate-normal-precision-and-covariance-parameterizations/ Two things are motivating this quick post. First, I have seen a lot of R code that is slower than it should be due to unoptimized sampling from a multivariate normal. Second, yesterday I spend a frustrating few hours tracking down a bug that ultimately was due to a slight subtlety in sampling from the multivariate normal parameterized by a precision matrix (the inverse of a covariance matrix). Key Idea: It is easy to draw univariate standard (e. http://statsathome.com/2017/06/01/sampling-covariance-matricies-with-fixed-total-variance/ Thu, 01 Jun 2017 00:00:00 +0000 stats.at.home@gmail.com (Justin and Rachel Silverman) http://statsathome.com/2017/06/01/sampling-covariance-matricies-with-fixed-total-variance/ Introduction I have been thinking a lot about the concept of Total Variance recently. Total variance (which can be defined as the trace of a covariance matrix) is a measure of global dispersion that has been particularly useful for me when building multivariate models. However, for some reason, I have yet to see this concept discussed much outside of compositional data analysis (see pg. 35 of Lecture Notes on Compositional Data Analysis) or Principle Component Analysis.