  We introduce a new method for high-dimensional, online changepoint detection
in settings where a $p$-variate Gaussian data stream may undergo a change in
mean. The procedure works by performing likelihood ratio tests against simple
alternatives of different scales in each coordinate, and then aggregating test
statistics across scales and coordinates. The algorithm is online in the sense
that both its storage requirements and worst-case computational complexity per
new observation are independent of the number of previous observations; in
practice, it may even be significantly faster than this. We prove that the
patience, or average run length under the null, of our procedure is at least at
the desired nominal level, and provide guarantees on its response delay under
the alternative that depend on the sparsity of the vector of mean change.
Simulations confirm the practical effectiveness of our proposal, which is
implemented in the R package 'ocd', and we also demonstrate its utility on a
seismology data set.
