Contributed Deconstructions: Irony & Bad Faith 3

My efficient Errorstat Blogpeople1 have put forward the following 3 reader-contributed interpretive efforts2 as a result of the “deconstruction” exercise from December 11, (mine, from the earlier blog, is at the end) of what I consider:

“….an especially intriguing remark by Jim Berger that I think bears upon the current mindset (Jim is aware of my efforts):

Too often I see people pretending to be subjectivists, and then using “weakly informative” priors that the objective Bayesian community knows are terrible and will give ridiculous answers; subjectivism is then being used as a shield to hide ignorance. . . . In my own more provocative moments, I claim that the only true subjectivists are the objective Bayesians, because they refuse to use subjectivism as a shield against criticism of sloppy pseudo-Bayesian practice. (Berger 2006, 463)” (From blogpost, Dec. 11, 2011)
_________________________________________________
Andrew Gelman:

The statistics literature is big enough that I assume there really is some bad stuff out there that Berger is reacting to, but I think that when he’s talking about weakly informative priors, Berger is not referring to the work in this area that I like, as I think of weakly informative priors as specifically being designed to give answers that are _not_ “ridiculous.”

Keeping things unridiculous is what regularization’s all about, and one challenge of regularization (as compared to pure subjective priors) is that the answer to the question, What is a good regularizing prior?, will depend on the likelihood.  There’s a lot of interesting theory and practice relating to weakly informative priors for regularization, a lot out there that goes beyond the idea of noninformativity.

To put it another way:  We all know that there’s no such thing as a purely noninformative prior:  any model conveys some information.  But, more and more, I’m coming across applied problems where I wouldn’t want to be noninformative even if I could, problems where some weak prior information regularizes my inferences and keeps them sane and under control.

Finally, I think subjectivity and objectivity both are necessary parts of research.  Science is objective in that it aims for reproducible findings that exist independent of the observer, and it’s subjective in that the process of science involves many individual choices.  And I think the statistics I do (mostly, but not always, using Bayesian methods) is both objective and subjective in that way.  That said, I think I see where Berger is coming from:  objectivity is a goal we are aiming for, whereas subjectivity is an unavoidable weakness that we try to minimize.  I think weakly informative priors are, or can be, as objective as many other statistical choices, such as assumptions of additivity, linearity, and symmetry, choices of functional forms such as in logistic regression, and so forth.  I see no particular purity in fitting a model with unconstrained parameter space:  to me, it is just as scientifically objective, if not more so, to restrict the space to reasonable values.  It often turns out that soft constraints work better than hard constraints, hence the value of continuous and proper priors.  I agree with Berger that objectivity is a desirable goal, and I think we can get closer to that goal by stating our assumptions clearly enough that they can be defended or contradicted by scientific theory and data—a position to which I expect Deborah Mayo would agree as well.

(see also Gelman’s blog)

_________________________________________________

Davidjrohde:

This comment was published in Bayesian analysis which has an obviously specialist audience, the two articles and the comments on the two articles reveals a near unanimous preference for subjective Bayes as the foundations of statistics.  To this narrow specialist audience “subjective” is a complement, an idealized limiting case of an optimal statistical analysis.  If you have a philosophical objection to subjective Bayes (or Bayes in general) as the foundations of statistics then you are really far outside the target audience and understandably the comment will be opaque.

I think Berger is saying that an objective Bayesian might understand the consequences of diffuse priors better than a subjective Bayesian, he is probably employing both Bayesian and non-Bayesian criteria to investigate the consequence of priors, making objective Bayes a bit of a piece meal “theory”.  My reading of the article is that Berger is a subjectivist, who is promoting tools outside standard subjective Bayesian theory (objective Bayes and frequentist) on practical grounds, it is interesting that the more extreme objective Bayes arguments of Jefreys and Jaynes seem to be largely abandoned now.

Of course the article reveals differences in Bayesians, but I think also reveals a remarkable convergence of opinion.  Subjective Bayes is the foundations of statistics, but in an operational sense fully specifying subjective probabilities and then conditioning on observables is not remotely practical.  Berger and Goldstein suggest different tools for dealing with this problem and the debate is largely carried out within this context (excluding Wasserman’s comments).

_________________________________________________

Eileens34:

My guess is that there is a typo, and Berger meant to say  “the only true objectivists are the objective Bayesians…” in the quote above.  Mystery solved!

_________________________________________________

Deborah Mayo (from blogpost, December 11, 2011):

How might we deconstruct this fantastic remark of Berger’s?5  (Granted, this arises in his rejoinder to others, but this only heightens my interest in analyzing it.)

Here, “objective Bayesians” are understood as using (some scheme) of default or conventionally derived priors.  One aspect of his remark is fairly clear: pseudo-Bayesian practice allows “terrible” priors to be used, and it would be better for them to appeal to conventional “default” priors that at least will not be so terrible (but in what respect?). It is the claim he makes in his “more provocative moments” that really invites deconstruction. Why would using the recommended conventional priors make them more like “true subjectivists”?  I can think of several reasons—but none is really satisfactory, and all are (interestingly) perplexing. I am reminded of Sartre’s remarks in Being and Nothingness on bad faith and irony:

“In irony a man annihilates what he posits within one and the same act; he leads us to believe in order not to be believed; he affirms to deny and denies to affirm; he creates a positive object but it has no being other than its nothingness.” (Sartre)

So true!  (Of course I am being ironic!) Back to teasing out what’s behind Berger’s remarks.

Now, it would seem that if she did use priors that correctly reflected her beliefs (call these priors “really informed by subjective opinions”(riso?), and that satisfied the Bayesian formal coherency requirements, then that would be defensible for a subjective Bayesian. But Berger notices that, in actuality, many Bayesians (the pseudo-Bayesians) do not use riso priors. Rather, they use various priors (the origin of which they’re unsure of) as if these really reflected their subjective judgments. In doing so, she (thinks that she) doesn’t have to justify them—she claims that they reflect subjective judgments (and who can argue with them?).

According to Berger here, the Bayesian community (except for the pseudo-Bayesians?) knows that they’re terrible, according to a shared criterion (is it non-Bayesian? Frequentist?). But I wonder: if, as far as the agent knows, these priors really do reflect the person’s beliefs, then would they still be terrible? It seems not. Or, if they still would be terrible, doesn’t that suggest a distinct criterion other than using “really informed” (as far as the agent knows) opinions or beliefs?

Berger, J. (2006),“The Case for Objective Bayesian Analysis”, and “Rejoinder”, Bayesian Analysis 1(3), 385–402; 457-464.

Sartre, J.P Being and Nothingness: an essay in phenomenological ontology (1943, Gallimard); English 1956, Philosophical Library Inc.

[1] This  is totally unrelated, I think, but the crew from Elba have wanted me to blog about some symbiotic worm one of them studies in Elba.  I don’t know if there is a suggestion of an analogy between a symbiotic relationship between objective and subjective Bayesians , but I really prefer not to blog about worms, or even think about them (this footnote is all**).  The truth is, I used to dig for worms with my brother when we were kids, but then had some bad experiences in Ferndale one summer. Sorry guys, start  a blob blog of your own.

**Here’s a website: http://www.youtube.com/watch?v=rxEC4CVswYI

[2] Strictly speaking, you could submit your creative attempts by Wednesday, Dec. 28, and of course, you can always comment, as I will.  There were 4 other contributions which are fine as comments, more than deconstructions.

Categories: Irony and Bad Faith, Statistics, U-Phil | Tags: , , , | 11 Comments

Post navigation

11 thoughts on “Contributed Deconstructions: Irony & Bad Faith 3

  1. Daniel Lakeland

    I am interested in your blog but I find the typography so incredibly distracting and difficult to read that I simply pass it over usually. Fonts are too tiny to see, background colors change randomly between body text and quotes, body text in bold, the body has a fixed width that doesn’t scale with the window size and is too wide for comfort. I would recommend a little professional consultation with a web design expert to get things to be more comfortable for your blog readership.

    • Yes, I said it was a rag tag blog, where we are still experimenting. Making the font larger is easy enough though. I would need to find a web professional, I guess, if I continue this activity. I had thought it helped to have quotes with a different color to set them off. that’s what I’ve seen on other blogs. We can go back to a more narrow width, I agree. The only reason we went wider was so that comments wouldn’t be so scrunched. So I guess those reading, nevertheless, are really hard-core folks. Thanks!

      • Paul Healey

        You did something helpful here. Still I think some typographical attention is probably in order.

        As for substantive comments: It’s not clear to me what it means *really* to be an Objective Bayesian vs a Subjective Bayesian. The fact is that a Bayesian analysis involves using a certain mathematical form: P(A|B) = P(B|A) P(A) / Z.

        We’re forced to choose P(A) and we can do so in a way that represents some knowledge of A or we can choose it in a way that is some kind of default. Generally to incorporate a lot of knowledge requires a lot of work but it is possible to encode various important pieces of knowledge without a lot of work. That’s the role of “weakly informative” priors.

        In many problems we have some general purpose knowledge about certain parameters. For example that they may be positive only, that they may take on values that are generally within some broad range (for example, if we pre-scale by what we think are some “typical” values, then we may expect the result to be in a range around 0.1 to 10 with a peak near 1). On the other hand, we may prefer not to truncate the effect of the likelihood so we prefer to use some kind of exponential tailed distribution which has support on all of the positive real line.

        That kind of thing keeps us from getting ridiculous results that contradict basic knowledge that we have. Doing this “weakly informative” version of Bayesian analysis produces an analysis that large swaths of people can agree with: anyone who suggests that negative variances are a good results can be immediately ignored for example. As soon as you try to get super-subjectivist and encode a prior that represents more than “general knowledge” about the process however, your analysis becomes less and less useful to others as they can reasonably disagree about the details

  2. TGGP

    I believe the December 11 blogpost referenced is this one. I link so that it will be easier to find when it is in the more distant past.

    • TGGP: Thanks, are you saying my blog should use an “about” page? The easiest thing is just a link within the post. I deliberately rewrote all the relevant parts of my Dec 11 post on the current one, figuring that people wouldn’t want to go looking. My Elbian Blog Administrators are on break this week.

      I never claimed this was anything but a rag tag blog; I frankly view myself as an artist and philosopher, and in any event, would likely start to question this little experiment entirely if I found myself needing to have a little consultation with a web design expert (my blogposter’s feelings are a bit hurt at this insinuation). Once back at Elba in a few weeks, this would mean even more ferry trips to the island,which I’m loathe to undertake.

      But really, these blogspotting things tend to have minds of their own—the preview doesn’t even resemble the final look—and, most importantly, there’s a limit to how much time I can spend fooling with body size, indents, fonts–after I’ve already put a fair amount of thought into the content—what I intend as the main rationale and contribution of this blog. Someone said the the posts were too wide, but this was because some others called for greater width for the comments,and anyway, Gelman’s blog is wider—I took his as a model.

      At least 6 people have written to me on e-mail today and yesterday with interesting substantive remarks/questions; I wish they would be less reluctant to post (anonymous is fine). Metablogging remarks are ok, but not as vital as substantive ones. Comments are open and not monitored.

      Fortunately, as I discovered recently, there are “stats” kept on the blogs, and there seems to be a good-enough number of people tuning in…suffering, as they must be, as they slog through scary random changes of color and withstand the cruel discomforts of an overly wide body (of text) just to grab at some insights. These tortured ones, eyes tearing to make out the tiny letters—groping, grasping, fearlessly making their way forward, all in order to unearth, at last,finally! some tiny morsels of light in these darkly battered statistical fields….All praise goes out to these steadfast ones!

      • TGGP

        I hadn’t even noticed the lack of an “about” page.

        I like to follow back-links to see how a conversation developed. Googling snippets of text and adding a link is just a habit of mine.

        UPDATE: Ah, right after I posted this comment I noticed what you are referring to. Disqus adds that above all the comments I make through them. I am so used to it I don’t give it any thought. I don’t even have much info at my about page, I just didn’t feel like writing much for my Disqus profile.

      • TGGP:Having links within a blog, to previous blogposts, is a very good idea, I’m recommending my blogpeople institute this—better than merely referring to dates. I don’t understand your “UPDATE” sorry. Disqus adds what? Frankly I try never to go into disqus if I can avoid it, it seems to be some kind self-referential commentary feature living symbiotically within an existing blog commentary feature, or a potential one. I’m not sure why we’re not using the Google comments facility, unless there’s a problem with it.

  3. Daniel Lakeland

    Also I have previously tried to comment on this blog but it wouldn’t accept my OpenID. something you’re doing now allows me to comment using my OpenID, that’s a bonus.So the technology is progressing… However my other comment that I just put up doesn’t show up, and comments that I made a few hours ago (maybe 4) are now listed as having been put up 12 hours ago? Your reply to my comment has disappeared. I think perhaps there is something technologically challenged about the current state of your small island ;-)

    • Daniel: It’s so great to have your continual meta-blogging remarks–and yes, many people feel we are technologically challenged on Elba—such is the life of exile–but we do have the best research center on that symbiotic worm I mentioned.
      So far as I know, we haven’t done anything different wrt “open ID”, whatever that is, but I’m glad you think we’re making a bit of technological progress, even if it is at a worm’s, I mean snail’s, pace.
      I have no idea where my initial reply to you has gone, I have sent a message to the Blogsfolk, I know they’re trying to work on all of the problems you mentioned yesterday. Still, I think my final paragraph to TGGP, which is still there, expresses my attitude. I might just resort to either plain pages with no background, or quit altogether!

I welcome constructive comments for 14-21 days

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Blog at WordPress.com. The Adventure Journal Theme.

Follow

Get every new post delivered to your Inbox.

Join 409 other followers