Let's give it a second thought
This is my first attempt at blogging.After ten years of applied Bayesian work in phylogenetics and in evolutionary genetics, I feel the need to step back and re-think the whole thing.Undoubtedly, since...
View ArticleBreathing some fresh air outside of the Bayesian church
In a recent post, Larry Wassermann asks whether Bayesian inference is a religion. He goes on suggesting that, in itself, Bayesian inference is not a religion. However, he says, there is a minority of...
View ArticleThe Bayesian agent as a heuristic model
The commonly accepted justification of Bayesian inference, in terms of subjective personal probabilities, coherentist arguments, dutch books and all that, is mostly due to de Finetti, Savage and...
View ArticleTwo sides of the same coin
One of the things that people want to do with phylogenies is to estimate parameters or test hypotheses about species diversification processes (Nee et al, 1992). The idea has been revisited recently,...
View ArticleMaximum marginal likelihood
In my last post, I mentioned the possibility of comparing alternative diversification models, conceived of as alternative priors on divergence times in a molecular dating context, using Bayes...
View ArticleHow to interpret posterior probabilities?
What does it mean, for instance, to report a posterior probability (pp) of 0.87 for the monophyly of a given group of species (say Archaea)? Intuitively, a stronger support than 0.82 and a weaker...
View ArticleCalibrated Bayes
Can we, under certain conditions, interpret posterior probabilities in frequentist terms? That is, such that, under controlled simulation settings, 95% of our 95% credible intervals across our...
View ArticleTwo well-calibrated cases
Before getting into challenging problems, let us have a quick look at two simple cases of Bayesian methods that appear to have good frequentist calibration properties. Both are Gaussian comparative...
View ArticleEmpirical Bayes and calibration
An obvious case where Bayesian inference has good frequentist properties is when the prior itself has a clear interpretation in terms of empirical frequencies.As a simple example to illustrate the...
View ArticleEmpirical Bayes and shrinkage
One thing I did not mention in my last post is that empirical Bayes is fundamentally a shrinkage approach.Shrinkage relates to the idea that you can improve an estimator by combining it with other...
View ArticleShrinking gene trees
A particularly interesting example of empirical Bayes in current phylogenetics is provided by the gene-tree species-tree reconciliation methods (Arvestad et al, 2003, Akerborg et al, 2009, see also a...
View ArticleThe empirical Bayes future of genomics
Empirical Bayes is the future of genomics. None explains this point more clearly and more convincingly than Brad Efron, in a book that should really belong to your personal library if you are into...
View ArticleThe adventurous Bayesian and the cautious Frequentist
Although the idea of controlling for false discovery rate (FDR) was first proposed in a purely classical context (Benjamini and Hochberg, 1995), the FDR has a simple empirical Bayes interpretation...
View ArticleOvercoming the fear of over-parameterization
I am always suprised to see many phylogeneticists and evolutionary biologists often so afraid of parameter-rich models. For some reason, nothing scares people more than the risk of overfitting the...
View ArticleSoft and hard shrinkage
Shrinkage based on hierarchical priors can be seen as a way of reducing the effective number of parameters of a model.Consider for instance the problem of allowing for amino-acid compositional...
View ArticleParameter estimation: optimizing versus conditioning
Misunderstandings about how Bayesian inference works are very common. In particular, people often don't understand that, in Bayesian inference, you do not have the problem of parameter-rich models...
View ArticleBlending p-values and posterior probabilities
Interesting column in Nature this week, by Regina Nuzzo, about p-values and why so many published findings are not true (see also Johnson, 2013, as well as many other earlier articles, e.g. Berger and...
View ArticleRevised standards: p-values and false discoveries
Since we are again talking about p-values, evidence and scientific false discoveries (see my last post), I would like to come back to Valen Johnson's article of last fall (Johnson, 2013). Even if the...
View ArticleWaking up from hibernation
This blog has not been very active lately.. I was too busy on other things. But there are still many different subjects that I would like to discuss here.Let me post one or two additional comments...
View ArticleFDR and the single-gene experiment
Imagine that you want to test for the presence of positive selection in a given gene in the human lineage, based on a protein alignment and using a codon model. Your data consist of aligned sequences...
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