We can think about our attitude towards Bayesian statistics along a kind of scale, or a group of related scales, for instance something like this:

1) Bayesian statistics is so wrong-headed that it is more likely to tend towards wrong results than correct results.

2) Bayesian statistics is no help at all in learning about anything.  The results are no better than random processes like rolling dice or a coin flip.  It's utterly worthless.  (Sidenote: this is actually worse than (1).  If (1) were the case, you could always bet against Bayesian statistics and come out on top!  Thus (1) would actually useful!)

3) Bayesian statistics can be one among many tools for gaining certain kinds of relevant knowledge, but it cannot function correctly unless it is used in combination with other conceptual tools.

4) Bayesian statistics is one tool among many, and there are certain specific applications where it becomes possible and useful to use Bayesian statistics without other conceptual tools - taking off the training wheels, so to speak.

5) Bayesian statistics is not only one tool among many, it is the best tool in the toolkit.  Sure, there may be certain tasks where it's not easy to use Bayesian statistics - maybe even impossible - and for such projects it will be necessary to use other tools.  But if and when it is possible to use Bayesian statistics, we should, because it's the most reliable guide towards the truth.

6) Even most of those projects in which Bayesian statistics seems currently impractical will one day be accessible to Bayesian modeling.  So we are gradually working towards a future in which Bayesian statistics and only Bayesian statistics is one truth path towards knowledge.

7) Bayesian statistics is omnipotent; it will bring omniscience.  

8) The word "truth" refers only to the results of Bayesian statistics.  Thus, by definition, only the results of Bayesian statistics are true.

Where do I stand on this scale?  Well, it depends on my mood.  In general, I would say that I have a vague suspicion that (5) might be true, but I am far from convinced, and indeed I can see many ways in which it might be false.  At heart, I am probably therefore somewhere around a (4), but to be safe, I think we should act as if (3) is actually the case.  I think I've seen enough evidence to show that (1) and (2) are mostly wrong, I think (6) is very probably wrong, and I utterly reject (7) and (8).  

(8) is the most dangerous position of all, even more dangerous than (7).  I maintain adamantly that to be valid, Bayesian statistics must be validated by something other than Bayesian statistics.

So I guess you can call me a moderate on Bayesian statistics.  I like it, but I don't worship it.

Bayesian statistics is pleasurable for people who enjoy quantifying things - which, I must say, is nice.  Numbers feel so good.

I guess the real question comes when you use more than one conceptual tool in the toolkit, and you come to different results.  Which one should you trust?  Bayesian statistics, or one of the other ones?

Okay, so first: what other ones?  What are the other methods available to us?  Well, most obviously, there's frequentism, the main competitor against Bayesianism.  There's also the classical model of probability, as articulated by Laplace and also Bernoulli - and there's some overlap between the classical model and Bayesianism, though of course Laplace and Bernoulli had not developed Bayes's theorem.  But I want to cast a wider net here.  Outside the realm of statistics, there's anecdotal evidence.  There's a priori reasoning.  There's also plain old common sense, and intuition.  There are also poetic truths, metaphorical truths, tradition, and so on.  There are many paths up the mountain.

If all of these other tools in the toolkit are pointing in one direction, but Bayesian reasoning is pointing in another, should we trust Bayes's theorem, or should we trust the rest?  I'm honestly not certain.

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