Professor Peter Congdon reports on two Bayesian models for global temperature shifts in his textbook, *Applied Bayesian Modelling*, as “Example 6.12: Global temperatures, 1850-2010”, on pages 252-253. A direct link is available online. The first is apparently original with Congdon, but the second is an adaptation of Thomson, Kimmerer, Brown, Newman, MacNally, Bennett, Feyrer, and Fleishman, “Bayesian change point analysis of abundance trends for pelagic fishes in the upper San Francisco Estuary”, *Ecological Applications*, **20**(5), 2010, 1431-1448.

The first model supports changes in levels, and assumes change points are uniformly distributed across the entire history. It finds three change points during 1850-2010, approximately in the years 1929, 1978, and 1996, dividing the history into four regimes, the first two being relatively downlevel, and the last two uplevel, with 1996-2010 being especially pronounced. This offers an alternative and intriguing interpretation of the data discussed both at the *Azimuth Project*, and especially results of Fyfe, Gillett, and Zwiers reviewed therein, and by Tamino. The results are robust against alternative uniform priors, still yielding 1929, 1978, and 1996 as change points. The *deviance information criterion* (“DIC”; see also here, here, here, and here) value for the model is -552 and *expected predictive deviance* (“EPD”) is 0.319.

The second model allows for changes in levels *and trends* following the work quoted by Thomson, *et al* above. Because of the additional capability in this model, it discerns level shifts in 1964 (having a level shift probability of 0.96, by the way), with less probable shifts in 1946, 1896, and 1877. The highest probability for a trend shift occurs in 1945, but has a probability of only 0.30. The model fit of this second model is better by DIC, having a value of -558, and the EPD agrees, but slightly, having a value of 0.318.

A logical third model would be to only allow changes *in trends* rather than levels and trends. I’ll probably do that and write that up here some day, using the data Congdon provided.

By the way, the *BUGS* code is available for these examples in the package associated with Professor Congdon’s textbook.

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## About hypergeometric

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