A really great into to the subject is Michael McCarthy's "Bayesian Methods for Ecology". Also highly recommend Kery's 2 books "Introduction to Winbugs for ecologists" and "Bayesian population analysis using Winbugs". But McCarthy's book is a great into to the subject.

in contrast to some other references, I like the approach by Benjamin M. Bolker: Ecological models and data in R, in the respective chapter. A very hands-on approach that I have only had a superficial look at yet seems to be provided by Jim Albert: Bayesian computation with R. Will probably get the whole book soon

Hi Alain,

The book by Albert that Susanne mentioned is part of the Use R series and it is very useful as an intro to Bayesian analysis, with lots of useful R code snippets:

http://www.amazon.com/Bayesian-Computation-R-Use/dp/0387922970

Another good hands-on text book with an ecological focus is the one by Marc Kery

http://www.amazon.com/Introduction-WinBUGS-Ecologists-Bayesian-regression/dp/0123786053

If you're serious about using Bayesian methods you should get hold of WinBugs or OpenBugs. Kery's approach is to use R as an interface to access the Bugs algorithms but you can use R itself for fairly heavy duty Bayesian analysis, and WinBugs can be used without R.

Before you invest the time and effort needed to lean these programming tools though I'd spend some time reading about the background theory and philosophy of Bayesian inference and ask yourself what it is that adopting a Bayesian approach will give you that frequentist approaches won't. Howson and Urbach's book on scientific reasoning in a Bayesian framework is a good introduction, but bear in mid that these guys are pro-Bayes and openly trying to convince the reader that it's the superior approach:

http://www.amazon.com/Scientific-Reasoning-Bayesian-Colin-Howson/dp/081269578X/ref=sr_1_1?s=books&ie=UTF8&qid=1381617119&sr=1-1&keywords=Howson+Urbach+Bayesian

Hope this helps

N

A really great into to the subject is Michael McCarthy's "Bayesian Methods for Ecology". Also highly recommend Kery's 2 books "Introduction to Winbugs for ecologists" and "Bayesian population analysis using Winbugs". But McCarthy's book is a great into to the subject.

thank you all for these references. Neil's comment is very important: what is the contribution of Bayesian statistics over more traditional approach? Results can be compared? And if the different results, what should we choose?

Frequentist approaches estimate the frequency with which data would be observed with replicated sampling, assuming the hypothesis under investigation is true. Bayesian methods, on the other hand, permit probabilistic statements about the hypotheses themselves (e.g. the probability that a particular hypothesis is true). Bayesian approaches also allow the formal incorporation of prior information about a system. We often have this information, e.g. from pilot/independent studies, and in my mind it doesn't make sense to pretend it doesn't exist. (Although of course the results of frequentist hypothesis-testing are often assessed - less formally - in the context of previous work.)

I second Peter's recommendations of McCarthy 2007, and of Kery's two books. They are both easy reads and great introductions to Bayesian techniques. McCarthy's book has a couple of introductory chapters that give some background about the philosophy and logic of Bayesian methods, and compares and contrasts to frequentist methods. Kery's books present examples of ecological modelling problems, and explore them through simulation of data (in R) and subsequent model-fitting by Maximum Likelihood, and by WinBUGS (Bayesian).

As to your final question, Mick McCarthy cites E.T. Jaynes: "... Bayesian and frequentist methods often generate numerically similar answers ... However, Bayesian methods have the distinct advantage that when the numerical results differ, the Bayesian methods are invariably correct (Jaynes, 1976)."

It doesn't all have to be Bayesian. However, an advantage of Bayesian methods is the flexibility and relative ease of fitting hierarchical models (ie. where the parameters you are estimating are themselves drawn from distribution with higher-level hyper-parameters). For example this is certainly the case with the species richness models described in this recent paper of Iknayan et al.

http://dx.doi.org/10.1016/j.tree.2013.10.012