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<\/p>\nBayesian statistical have become very popular in the last 5 to 10 years amongst environmental scientists, due to their much greater flexibility than conventional frequentist approaches. They also have an intuitive appeal: many people still incorrectly mis-interpret p-values, thinking that they are testing the significance of a hypothesis, when of course in reality they are giving the probability of the data, given the null hypothesis. This \u2018back-to-front\u2019 approach of the traditional methods also causes problems for students learning statistical methods.<\/p>\n
Several excellent books have been published in the last few years on Bayesian stats, aimed at ecologists. I particularly like the approach taken by Marc Kery and colleagues, who now have now published three texts on the subject.<\/p>\n
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You\u2019ll have spotted that the most recent book has \u2018Volume 1\u2019 in the title, so we look forward to the second volume in the series. As you\u2019ll have guessed from the titles, the difficulty and complexity of the models increases with each book. If you\u2019re new to Bayesian stats, start with the Introduction to WinBUGS for Ecologists. This covers models which could mainly be done with standard frequentist statistics (some of the mixture-models described in the last chapters would be tricky however). A big advantage of this approach is that the book initially covers straightforward analyses using the linear model lm<\/span><\/span> command, examines the outputs, and then shows the identical analysis done from a Bayesian approach. This approach rapidly illustrates the much \u2018richer\u2019 amount of information that can be obtained from a Bayesian rather than frequentist approach. So the book shows how to calculate a mean (yes, I know that sounds trivial, but still useful), equivalent of a t-test (but via lm<\/span><\/span> for the frequentist method), one- and two-way anova, regression, glm, and mixed-effects models. Yes, all these can be done by conventional methods. If I\u2019m doing a simple regression, I\u2019ll still use lm<\/span><\/span> rather than writing BUGS code, but as a way of describing Bayesian methods its clarity is difficult to fault.<\/p>\n As you might expect, all the R code for the analyses described in the book can be downloaded from the web. But intriguingly, not the datasets. This is because Kery has a bottom-up approach to the data (see pages 7 and 8 of his introductory book):rather like a motorbike mechanic, you can only fully understand how the motorbike works if you have assembled all the pieces together before riding off on it. Likewise with a model: Bayesian models can become complex, so rather than presenting the reader with a set of data to analyse, the reader creates a set of data with known properties (mean, sd etc.), which is then assembled for modelling. Then the reader can look at the output of the model, and see how well it matches the original inputs. This avoids the \u2018black-box\u2019 problem of not understanding what the model is up to. It isn’t really needed for a simple familiar model like the Bayesian regression we’re about to discuss here, but for complex mixture, hierarchical random-effects or state-space models it seems an excellent method to test that your Bayesian code, in BUGS, JAGS, Stan or Greta, is doing what you think it should, before trying it out on real data.<\/p>\n The book uses WinBUGS, although the code works fine for OpenBUGS (still under active development), and with minor tweaks for JAGS. More changes would be needed for Stan, the newest Bayesian framework. I\u2019ll admit here that there are a number of things that I strongly dislike about existing Bayesian methods:<\/p>\n You have to learn yet another language. BUGS, JAGS and Stan all have a different syntax to R, with slightly different function names etc.<\/p>\n<\/li>\n You have to write a set of instructions to an external text file outside of R, which is then called via the relevant R library (e.g.\u00a0R2OpenBUGS) to carry out the Bayesian analysis.<\/p>\n<\/li>\n The BUGS\/JAGS\/Stan instructions cannot be debugged readily in R: it is fired off in one block for Bayesian analysis making debugging tricky with complex models. If you use RStudio, the IDE simply sees the code as a block of text and so ignores it.<\/p>\n<\/li>\n<\/ol>\n\n
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