John Baez at *The Azimuth Project* opened a discussion on the recent paper by Reid, *et al*

Philip C. Reid et al, Global impacts of the 1980s regime shift on the Earth’s climate and systems, Global Change Biology, 2015.

I was going to publish the material below there, but the *Azimuth* blog would not accept it for some reason, so I’m putting it here and placing a link.

The reason why RJMCMC is typically preferred is that the model for changepoints in a series depends upon the number of changepoints. Reversible Jump MCMC allows the stochastic search to jump among alternative models as well as find parameters within one, here these being *where* the changepoint is, as well as other parameters.

In this case, it’s a little more complicated because there is an ensemble of time series to consider, and the change points in question need to be common.

I am working on a write-up with accompanying code for this problem. It’s very much a preliminary draft, but there’s no reason why *Azimuth* readers can’t follow along in the development: https://goo.gl/bVnEHJ (Updated 19:19 ET, 3 Dec 2015.) Caution that this stuff is very much in progress.

By the way, at least in **R**, you don’t need to go back to Green 1995 for implementation. There are several **R** packages that will do this for you, and there are excellent write-ups available explaining RJMCMC with sample problems. A book I particularly like has a chapter devoted to the question, namely, R. King, B. J. T. Morgan, O. Gimenez, and S. P. Brooks, *Bayesian Analysis for Population Ecology*, 2010.

Some write-ups about changepoint detection in **R** are:

- http://things-about-r.tumblr.com/post/106806522699/change-point-detection-in-time-series-with-r-and
- http://qualityandinnovation.com/2015/07/14/a-simple-intro-to-bayesian-change-point-analysis/
- http://gallery.rcpp.org/articles/bayesian-time-series-changepoint/
- http://www.jstatsoft.org/article/view/v023i03
- http://www.lancs.ac.uk/~killick/Pub/KillickEckley2011.pdf
- http://arxiv.org/pdf/1309.3295.pdf

There is an online repository featuring links to software and publications. It’s a little weak on state-space methods, which is the way I think about series these days. In fact, the developing paper is heading in the direction of viewing a group of M series as M dimensions in an observational state, and using models of *seemingly unrelated time series* to track them, and look for regime shifts. Change points are detected by looking for large point decreases in the log-likelihood of the multivariate model.

I’ll explain more in the developing white paper. I to try what I’m developing on the 72 time series from Reid, *et al* used in their paper. I’m working with synthetic series to start. I probably should do theirs. I’m also working on similar ensembles of series, but all hydrological, from the Town of Sharon, MA. From my studies, there’s nothing technically new about the methods I am using. They may be unfamiliar, but they have a long and honorable history. (There’s also a forecasting and econometrics perspective given here.)

*Update*, 21^{st} December 2015

An update on the key problem concerning the water supply in the Town of Sharon by Paul Lauenstein can be found here.