A Welford accumulator for sample mean and variance

A simple class for keeping track of the running mean and the sum of squared deviations from the mean for a vector.

Usage

Welford(dn, means, vars)

# S3 method for class 'Welford'
update(object, newdata, ...)

Arguments

dn, means, vars: initialization of the Welford object: if means and vars are given, they are treated as the running means and variances, and dn is their associated sample size, and if not, dn is the dimension of the vector (with sample size 0).
object: a Welford object.
newdata: either a numeric vector of length d, a numeric matrix with d columns for a group update, or another Welford object with the same d.
...: additional arguments to methods.

Value

an object of type Welford: a list with four elements:

n: Running number of observations
means: Running mean for each variable
SSDs: Running sum of squared deviations from the mean for each variable
vars: Running variance of each variable

Methods (by generic)

update(Welford): Update a Welford object with new data.

Examples


X <- matrix(rnorm(200), 20, 10)
w0 <- Welford(10)

w <- update(w0, X)
stopifnot(isTRUE(all.equal(w$means, colMeans(X))))
stopifnot(isTRUE(all.equal(w$vars, apply(X,2,var))))

w <- update(w0, X[1:12,])
w <- update(w, X[13:20,])
stopifnot(isTRUE(all.equal(w$means, colMeans(X))))
stopifnot(isTRUE(all.equal(w$vars, apply(X,2,var))))

w <- Welford(12, colMeans(X[1:12,]), apply(X[1:12,], 2, var))
w <- update(w, X[13:20,])
stopifnot(isTRUE(all.equal(w$means, colMeans(X))))
stopifnot(isTRUE(all.equal(w$vars, apply(X,2,var))))