Counterpoint:

Last time I fitted a Bayesian model, I had 1 processor with some interpreted code and left it for ten minutes. YMMV.

Absolutely. Not all applications of Bayesian analysis are computationally-intensive. In some cases (an example: finding of single-nucleotide polymorphisms in next-gen sequencing data), Bayesian analysis comes down to multiplying prior probability of a SNP (for humans, 0.001 per genome position) by a few other numbers from the data itself to obtain posterior probability, which can be done in a linear time in a few minutes on tens of gigabytes of NGS data. And the best part is, no Bonferroni adjustment bullshit!

Hey, don't forget the Benjamini-Hochberg replacement for Bonferroni. The situation is not 'that' bad.

5. Bayesian analysis is too easy. You don't have to transform the data in any convoluted way, you just describe your model and crank the handle. Publishers will no longer be able to sort the sheep from the goats.

Ha ha. Yes, it is a bit like that. If somebody could just replace that pesky mcmc convergence crap with something that worked, or give me a quantum computer, then I would convert my models Bayesian overnight.

priors acknowledge subjectivity.

I think about this point someone should link to [share likelihood ratios, not posterior beliefs](http://www.overcomingbias.com/2009/02/share-likelihood-ratio...)... the summary is that you can do your Bayesian analysis without specifying the prior and just report the resulting likelihood ratios, telling everyone, "Here are the likelihood ratios, update your beliefs appropriately." Though that may lack some practicality.

Also, this is true, but I think it doesn't disagree with my point.

I just dread the length of my Own Risk and Solvency Assessment (ORSA) after Solvency II (the regulations for insurance companies in Europe) takes hold next year, if I have to explain the origins of my priors.

I actually think we could do some fuck-awesome work in evaluating our risk capital requirements using priors on all of of our inputs, and the computational requirements would not be 'that' frightening, given the valuations are all Monte Carlo anyway. It's not happening, yet, though.

A point by point rebuttal.

1. The op knows this but is implicitly believing his audience is different from the cited fields often enough to make point (1) relevant. Moreover, it's perfectly correct to say that many journal reviewers are not interested in Bayesian methods.

2.1. This is highly anecdotal and not at all a strong point. I'm sure Efron has knocked out a 600 core cluster doing frequentist bootstrapping (1). I'm also certain that many, many Bayesian methods run near instantly on modern hardware. I'll concede that there are fewer closed form results, though.

2.2 This is very true. Entrepreneurs?

3. "Data so sparse, expert judgement so rich" is exactly where Bayesian analysis is most pertinent. Use a prior to clarify and quantify your expert opinion and then demonstrate that indeed your few observations are worthy to change someone's opinion.

4. Choice of frequentist testing regime introduces subjectivity, too! Moreover, since these have been heralded as "objective" for so long it's pretty difficult to get people to recognize as much. Oftentimes, a frequentist method will be equivalent to a Bayesian method under a maximally uninformed prior. This is still a subjective assumption (though there are benefits of such a prior).

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Frequentists test are oftentimes very necessary. They have already been highly optimized in many cases and thus are available on low resource computing platforms. They are definitely an important engineering solution! That said, Bayesian methods do a far better job being clear in their assumptions and simple in their logic.

There is certainly room for better software (free or otherwise) to replace BUGS/JAGS/whatever for the largest use cases of statistics in many fields. Also, another point you make about Bayesian methods making life difficult during certification and publication is exactly right, and probably the largest (unspoken) reason why they're not going to be used in core scientific fields for a long while.

But both of those reasons are distinctly practical and unscientific. Bayesian methods do a better job using your data. They do this by allowing expert knowledge to enter into statistics in a sensible fashion. Finally, they introduce an easily understood interpretation on the answers to your statistical questions.

You might not personally want to use them today for practical reasons, but the author of this article is very much in the right to try to encourage more scientists in more fields to take a look.

(1) Sorry, I'm actually not at all sure if this is the case. Bootstrapping is still more computationally efficient than MCMC, I think. I just used the example because I think it's ridiculous to make either point.

3. I agree with your point in some instances - but in others there is a huge risk of building a complicated model that everybody trusts that is just a pile of twaddle; in which case the expert judgement would better stay in the experts' heads, or on the odd bar-chart. I have not noted this point in many statistics courses, but it is all over the actuarial courses.

1. And so the journal reviewers shouldn't be. They are interested in the results, and act like the financial or insurance regulator in making sure those results have been calculated in an unbiased manner.

4. Yes, choice of model introduces subjectivity. That two beers a day are alright doesn't imply I should have ten.

p.s. Does it not start life as an 'attempt at rebuttal'? 'Distinctly practical and unscientific'?, 'ridiculous'? I know it's the internet - but...

Apologies there, I was reacting to the exaggerated choice in anecdote, but actually meant the "practical" line favorably. Science and practicality can be at ends, but at the end, practicality wins by definition, right?

3. I agree that complex model building is fertile ground for hand-waving, this-is-too-complex-to-understand-so-just-accept-it false justification. I don't think large models are endemic to either Bayesian or Frequentist methods, though Bayesian methods do allow them to be built more easily. In both cases, I think simple sanity checks form a foundation that is necessary for the presentation of complex models.

1. I think the idea of being "interested in results" is a false hope. Experimentation does not always produce results, and when it does you probably don't even need statistics because the results are so obvious. In all other cases, uncertainty has become a major factor and demanding clarity is foolish. Tempting, but foolish.

4. I think under-modeling is dangerous, too. At the very least, it can rob you of the ability to quantify educated conclusions short of doing meta-analysis. At least with priors you're telling everyone you're a bit tipsy instead of stamping a bar chart down and having people swallow assumptions under the stamp of 'objectivity'.

It's kind of like Python 'import this'. Explicit is better.

Mcmc is what takes the time more tham the size of the model.

Definitely large models seem more likely to me in bayesian because it is so much neater to build them.

I notice that you are very fervent in your bayesianism, but please correct me if i read that wrongly. I was once at a conference in which a similar debate was ongoing at the lectern. Dr cox was main guest of the conf and when he was asked where he stood he said, and i misquote probably awfully from poor memory, that it was a bit silly arguing about it because you just used whichever was appropriate to the task at hand. I thought that was pretty cool.

I like Bayesianism because I think it's mathematically and philosophically cleaner. Then again, I think MCMC seems to show that it isn't so computationally clean. In realtime systems I am more than happy to use Frequentist models for their speed.

I suppose believe in a world where Bayesian methods are the primary didactic statistics useful in sciences and communication and Frequentist methods are used when closed form estimators are necessary and coherent with Bayesian estimates.

Or maybe an even better world where we have closed form, useful estimates from both camps.

Just think quantum computing. You could write down everything you know and every piece of data you have, eliciting by hand your utility and priors, and then press go on the mcmc. Awesome.

I agree with the general theme of the OP. Bayesian methods are technically better than frequentist methods.

However, like Betamax vs. VHS, there is more than just the technical correctness. Your point in 2.2 is the big one -- if there was a simple way to switch to Bayesian methods in existing statistics software like SPSS, that would be quite revolutionary. Right now, null hypothesis testing is too easy to do and widely accepted, even though the results may be completely wrong.