Following some discussions I had last week at Banff about data cloning, I re-read the 2007 “Data cloning” paper published in Ecology Letters by Lele, Dennis, and Lutscher. Once again, I see a strong similarity with our 2002 Statistics and Computing SAME algorithm, as well as with the subsequent (and equally similar) “A multiple-imputation Metropolis version of the EM algorithm” published in Biometrika by Gaetan and Yao in 2003—Biometrika to which Arnaud and I had earlier and unsuccessfully submitted this unpublished technical report on the convergence of the SAME algorithm… (The SAME algorithm is also described in detail in the 2005 book Inference in Hidden Markov Models, Chapter 13.)
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Over the two days of the Hierarchical Bayesian Methods in Ecology workshop, we managed to cover normal models, testing, regression, Gibbs sampling, generalised linear models, Metropolis-Hastings algorithms and of course a fair dose of hierarchical modelling. At the end of the Saturday marathon session, we spent one and half discussing some models studied by the participants, which were obviously too complex to be solved on the spot but well-defined so that we could work on MCMC implementation and analysis. And on Sunday morning, a good example of Poisson regression proposed by Devin Goodman led to an exciting on-line programming of a random effect generalised model, with the lucky occurrence of detectable identifiability issues that we could play with… I am impressed at the resilience of the audience given the gruesome pace I pursued over those two days, covering the five first chapters of Bayesian Core, all the way to the mixtures! In retrospect, I think I need to improve my coverage of testing as the noninformative case presumably sounded messy. And unconvincing. I also fear the material on hierarchical models was not sufficiently developed. But, overall, the workshop provided a wonderful opportunity to exchange with bright PhD students from Ecology and Forestry about their models and (hierarchical) Bayesian modelling.