Thus it seems quite reasonable to agree with both Gelman and Binmore, as I do. Or to put it another way, whilst, as you quote, Gelman refutes the objections in some settings (arguably, many) he does, as per your quote, accept them in others. Both sides of this coin matter.

]]>Bing bing bing, we have a winner….

Grasselli, pay attention. You may learn a thing or two. What applies in HIV tests may not apply in economics.

]]>2) When I quote people on the blog there usually is a link (in this case “Andrew Gelman” at the bottom of the quote is blued, and clicking on it you are directed to the original text).

3) Andrew Gelman — as probably everyone reading this blog knows — is a Bayesian of sort (and that’s — goes without saying — also one reason why it’s interesting to quote him when he is putting forward “inside” critique). But I think he is a much more qualified and open-mindede Bayesian than many others of the same ilk … In his article “Induction and Deduction in Bayesian Data Analysis” (http://www.stat.columbia.edu/~gelman/research/published/philosophy_online4.pdf), e. g., he writes:

“But I do not make these decisions on altering, rejecting, and expanding models based on the posterior probability that a model is true. Rather, knowing ahead of time that my assumptions are false, I abandon a model when a new model allows me to incorporate new data or to fit existing data better. At a technical level, I do not trust Bayesian induction over the space of models

because the posterior probability of a continuous-parameter model depends crucially on untestable aspects of its prior distribution. (For any parameters that are identifiable by the data, the behavior of the prior in the far tails of the distribution is irrelevant to inference within the model but can have arbitrarily large effects on the model’s marginal posterior probability.)”

Again I can’t but concur. ]]>

“Here follows the list of objections from a hypothetical or paradigmatic non-Bayesian:

Bayesian inference is a coherent mathematical theory but I don’t trust it in scientific applications.”

so it’s clear that “I” means “hypothetical non-Bayesian”. Instead, you removed the first sentence, so that anyone who didn’t read the article (for which you did not provide a link) would automatically (and rightly so) interpret “I” as “Andrew Gelman”.

It’s fine to quote from eminent statisticians, but why do so in a way that implies that they are criticizing Bayesian inference when, in fact, they are defending it?

]]>“Where do prior distributions come from, anyway? I don’t trust them and I see no reason to recommend that other people do, just so that I can have the warm feeling of philosophical coherence.”

that’s NOT Andrew Gelman’s opinion, but rather that of a hypothetical non-Bayesian that he created to voice the criticisms before he could respond to them.

You MUST know this, because at the start of the article, which can be found at

http://www.stat.columbia.edu/~gelman/research/published/badbayesmain.pdf

Andrew Gelman says:

“The present article is unusual in representing a Bayesian’s presentation of what he views as the strongest non-Bayesian arguments. Although this originated as an April Fool’s blog entry (Gelman, 2008), I realized that these are strong arguments to be taken seriously—and ultimately accepted in some settings and refuted in others.”

Why did you not quote this in your blog too? Were you trying to imply that the Objections to Bayesian Statistics are being raised by Andrew Gelman himself? Because that’s exactly what it looks like. You title your post Objections to Bayesian Statistics, remove all explanations from the original article clarifying that these are objection from a hypothetical non-Bayesian, and finish it with Andrew Gelman’s name, clearly implying that these are his opinions.

I find this to be irredeemably misleading, so I’m really interested to know your reasons for doing it.

Most importantly, however, are you going quote as prominently from the rejoinder article that Andrew Gelman wrote:

http://www.stat.columbia.edu/~gelman/research/published/badbayesresponsemain.pdf

whose abstract states: “In the main article I presented a series of objections to Bayesian in- ference, written in the voice of a hypothetical anti-Bayesian statistician. Here I respond to these objections along with some other comments made by four discussants.”

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