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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...

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Breathing 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...

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The 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...

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Two 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,...

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Maximum 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...

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How 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...

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Calibrated 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...

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Two 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...

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Empirical 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...

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Empirical 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...

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Shrinking 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...

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The 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...

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The 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...

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Overcoming 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...

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Soft 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...

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Parameter 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...

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Blending 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...

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Revised 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...

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Waking 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...

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FDR 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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