This is a chance for me to combine two of my interests–politics and statistics–and probably to irritate both halves of the readership of this blog. Anyway…
I recently wrote about the apparent correlation between Bayes/non-Bayes statistical ideology and liberal/conservative political ideology:
The Bayes/non-Bayes fissure had a bit of a political dimension–with anti-Bayesians being the old-line conservatives (for example, Ronald Fisher) and Bayesians having a more of a left-wing flavor (for example, Dennis Lindley). Lots of counterexamples at an individual level, but my impression is that on average the old curmudgeonly, get-off-my-lawn types were (with some notable exceptions) more likely to be anti-Bayesian.
This was somewhat based on my experiences at Berkeley. Actually, some of the cranky anti-Bayesians were probably Democrats as well, but when they were being anti-Bayesian they seemed pretty conservative.
Recently I received an interesting item from Gerald Cliff, a professor of mathematics at the University of Alberta. Cliff wrote:
I took two graduate courses in Statistics at the University of Illinois, Urbana-Champaign in the early 1970s, taught by Jacob Wolfowitz. He was very conservative, and anti-Bayesian. I admit that my attitudes towards Bayesian statistics come from him. He said that if one has a population with a normal distribution and unknown mean which one is trying to estimate, it is foolish to assume that the mean is random; it is fixed, and currently unknown to the statistician, but one should not assume that it is a random variable.
Wolfowitz was in favor of the Vietnam War, which was still on at the time. He is the father of Paul Wolfowitz, active in the Bush administration.
To which I replied:
Very interesting. I never met Neyman while I was at Berkeley (he had passed away before I got there) but I’ve heard that he was very liberal politically (as was David Blackwell). Regarding the normal distribution comment below, I would say:
1. Bayesians consider parameters to be fixed but unknown. The prior distribution is a regularization tool that allows more stable estimates.
2. The biggest assumptions in probability models are typically not the prior distribution but in the data model. In this case, Wolfowitz was willing to assume a normal distribution with no question but then balked at using any knowledge about its mean. It seems odd to me, as a Bayesian, for one’s knowledge to be divided so sharply: zero knowledge about the parameter, perfect certainty about the distributional family.
To return to the political dimension: From basic principles, I don’t see any strong logical connection between Bayesianism and left-wing politics. In statistics, non-Bayesian (“classical”) methods such as maximum likelihood are often taken to be conservative, as compared to the more assumption-laden Bayesian approach, but, as Aleks Jakulin and I have argued, the labeling of a political method as liberal or conservative depends crucially on what is considered your default.
As statisticians, we are generally trained to respect conservatism, which can sometimes be defined mathematically (for example, nominal 95% intervals that contain the true value more than 95% of the time) and sometimes with reference to tradition (for example, deferring to least-squares or maximum-likelihood estimates). Statisticians are typically worried about messing with data, which perhaps is one reason that the Current Index to Statistics lists 131 articles with “conservative” in the title or keywords and only 46 with the words “liberal” or “radical.”
In that sense, given that, until recently, non-Bayesian approaches were the norm in statistics, it was the more radical group of statisticians (on average) who wanted to try something different. And I could see how a real hardline conservative such as Wolfowitz could see a continuity between anti-Bayesian skepticism and political conservatism, just how, on the other side of the political spectrum, a leftist such as Lindley could ally Bayesian thinking with support of socialism, a planned economy, and the like.
As noted above, I don’t think these connections make much logical sense but I can see where they were coming from (with exceptions, of course, as noted regarding Neyman above).
I also thought of Fisher as a Libertarian, not Conservative.
Skepticism, scientific, social, or otherwise, is for me, inherently liberal.
This seems tied to me to psychology professor Bob Altemeyer's interesting claims that conservativism in the political spectrum is tied to a small authoritarian community aligned with a large population of people who want to be told what to believe (see http://home.cc.umanitoba.ca/~altemey/ for his interesting free book on the subject).
The term "conservatism" can mean a million different things. Wolfowitz Jr's passion for regime-change-all-around is hardly "conservative" in any classical sense.
In the UK there is a tradition of Radical Statistics, partly based on the theory that you can provoke change by describing the current situation accurately via statistics. You might, for instance, try to show the existence of poverty, or of discrimination.
For these purposes, I believe that frequentist statistics have an advantage over Bayesian statistics, because a Bayesian finding of inequality or poverty is always susceptible to the argument that it has been influenced by the prior chosen by the statistician.
It's funny. Most statisticians are actually fans of statism, neither liberal or conservative, although they may think they are.
Maybe I need not remind you the history of statistics. The early most important statisticians are also founders or supporters of eugenics. Galton, Pearson, Fisher, … great names, ha. Don't forget your friend in economics: Keynes. They are neither liberal or conservative.
The history of eugenics movement should be addressed in the first chapter of all the statistics textbooks. Seriously.
I find your typologies confusing.
Conservative = resistant to change
Liberal = pro change
Where do we fit Hayek, Friedman, or libertarians? They are hardly pro status quo.
Peter, Chris:
I agree that political attitudes are multidimensional. Still, I think there is typically some sense of a left-right divide.
Fernando:
I consider Milton Friedman etc. to be conservative in that they were economists who favored the existing economic order. They were not generally favor redistributive policies but rather were more likely to give reasons why it was OK for rich people to be rich. That's fine–and maybe such policies are good for non-rich people as well–but I consider them to be conservative.
Jflycn:
I agree that Galton is a hugely important figure in statistics and is discussed as such in Stigler's classic history of statistics book. You can go back further to Laplace, who did things for the French government. Should the history of statistics be discussed in statistics textbooks? Maybe. I don't know. If it is discussed, though, I agree that the historical and political context of these ideas is important.
Bayesianism is also multidimensional. I.J. Good (reprinted in Good Thinking) identified 11 dimensions and 46656 varieties of Bayesians.
The word "conservative" gets used many ways, for various political purposes, but I would take it's basic meaning to be someone who thinks there's a lot of wisdom in traditional ways of doing things, even if we don't understand exactly why those ways are good, so we should be reluctant to change unless we have a strong argument that some other way is better. This sounds very Bayesian, with a prior reducing the impact of new data.
I don't think one can say that Friedman "favored the existing economic order", since the existing economic order (now, and a few years ago when Friedman was alive) includes many, many state interventions that Friedman opposed.
Friedman always said it is others that called him "conservative" but he thought he was a "liberal" based on the same typology you mention.
cf. look at the economics of "liberals" in German politics. They are more of the free market people.
Two snippets:
it is foolish to assume that the mean is random; it is fixed, and currently unknown to the statistician, but one should not assume that it is a random variable.
Regarding the normal distribution comment below, I would say:
1. Bayesians consider parameters to be fixed but unknown. The prior distribution is a regularization tool that allows more stable estimates.
My comment–frequentists believe parameters to be fixed but unknown also–this "regularization" has some similarities of a probability of a probability (see Pearl, among others, as to why this is a bad idea). But the philisophical implications are astounding–prior beliefs have now been reduced to a fix for frequentist inference. Incidentally, since we're in the frequentist domain, shouldn't the covariance matrix of the Bayesian approach be negative definite (minus the frequency estimator)? Asymptotically, of course, everything should approach Fisher's information and one wouldn't notice a difference between the two approaches.
Rahul:
Yes, I'm using "conservative" in the U.S. sense.
Radford:
Regarding Bayes and conservatism, I agree with you completely (and maybe so did Xiao-Li's professors back in China, the ones who claimed that Bayes was contrary to Maoism).
Regarding Friedman: Everybody likes some government policies and dislikes others. Overall, Friedman tended to like the conservative (in the U.S. sense) economic policies and dislike the liberal ones. The conservative policies tended to reinforce the economic status quo. As you and I both noted above, reinforcing the status quo is not necessarily a bad thing!
Numeric:
To paraphrase an economist whose name was mentioned earlier in this thread: Aysmpotically we're all dead. I'd like to do some statistical inference while I'm still alive.
Are there any "real" examples where the two approaches (frequentist versus Bayesian )give grossly different results? Is this just a philosophical battle or a practical one? Sorry, if my question is naive.
Change is all relative. In order to define conservative in the sense of "resistant to change", you need to pin down a reference point. If our reference point is 1810, Bayesian stats hardly seems "liberal". In 1900, frequentism represented change. Given the success of that change, with a narrow enough historical window, frequentism looks conservative.
I'm guessing that propounding frequentist philosophy in 2050 will feel quaint, not conservative. By 2100, it'll just feel quirky. That is, I'm guessing it'll go the way of powdered wigs, which were pretty much de rigueur for gentelmen in 1780, on the wane in 1800, and passé by 1820. Nowadays a powdered wig would look bizarre rather than conservative.
Rahul:
Yes, practical issues are involved. You could read my books and articles for a bunch of applied examples.
As much as I admire Laplace, his political views are not a very nice aspect of him: he basically turned coat at each change of regime, from Napoleon (to whom he taught) to Louis XVIII, in order to keep his privileges and titles…
What were Thomas Bayes's politics?
Overall, Friedman tended to like the conservative (in the U.S. sense) economic policies and dislike the liberal ones. The conservative policies tended to reinforce the economic status quo.
Either of these sentences is arguably true, but not both! One might define "conservative policy" to be close to what Friedman liked, but if so, these policies do not reinforce the economic status quo, which is heavily dependent on the sort of state interventions that Friedman opposed. But of course, if by "conservative" you mean "reinforces the status quo", then the second sentence is tautologically true.
Bayes was non-conformist, and keen on Arianism
Rahul, Lindley's paradox is a good example of Bayesian vs. frequentist approaches yielding difficult to reconcile results: http://en.wikipedia.org/wiki/Lindley%27s_paradox
Radford:
The economic status quo is that Thurston Howell III has a million dollars and Gilligan doesn't.
Many argue Friedman was the intellectual motor behind Thatcher & Reagan's "revolutions". Not E. Burke's cup of tea.
Last time I checked, the status quo circa 1970 involved top marginal tax rates of >80%, a lot of trade protection and corporatist policies.
But my point is more general. According to your definition anybody who likes change, progress etc is a liberal, everyone else a staid, rancid conservative. I beg to differ.
Btw if you move from:
Conservative = resistant to change
To
Conservative = U.S. conservative
Then I suspect you've completely changed the terms of the debate.
I read Andrew's comments about status quo to refer to the actual wealth distribution, not the policies in place at the time: a liberal policy in that sense would be one that tries to actively redistribute wealth, or tries to change the means by which one makes money. Thus to the extent that a currently rich person would remain rich, or a wealth producing occupation would remain valuable, a policy is deemed "conservative".
It's also worth noting that conservatism is not measured against policies in place at the moment, but by "traditional" policies. Otherwise conservative would just be the dominant policy of the day. Thus though the 70's had a high marginal tax rate, that had only been true for ~40 years. In terms of philosophical development, that's not a long time. But of course, you can choose all sorts of time frames to define liberalism and conservatism and get all different sorts of results.
Radford:
The economic status quo is that Thurston Howell III has a million dollars and Gilligan doesn't.
I suspect there's a literary reference I'm missing here, since I don't know who either of these people is, but anyway, my point is that Friedman's policies certainly do not reinforce the economic status quo. I don't think this is controversial. Does anyone believe that implementing Friedman's preferred policies would leave things pretty much unchanged? Opinions differ on whether they would lead to a new era of prosperity for all, or a new era in which the rich are even richer, and the poor and middle class descend into destitute servitude, but I don't know of anyone who thinks they would have no significant effect.
If you define conservative as someone who likes inequality and liberal someone who wants less inequality, that is fine. Definitions are definitions.
But then I don't think the definition rhymes with the points about resistance to change that I think Prof Gelman is trying to make. (But I may have misinterpreted his post.)
In passing, inequality has increased over the past decades. The status quo in the post war years was one of significant equality relative to today. Maybe (I speculate) this is the change "conservatives" like Thatcher or Reagan wanted to bring about.
Perhaps better two have 2 dimensions: Left- Right and pro change pro status quo. Then see on what quadrants Bayesians and classicists fall. Maybe Bayesians ought to be (Left, pro s.q.)and Classical (Right, pro s.q.) or (Right, (pro s.q. & pro change)). I don't know.
"The history of eugenics movement should be addressed in the first chapter of all the statistics textbooks. Seriously."
Indeed.
In general, the entire statistical turn of mind in the human sciences — the ability and desire to notice patterns among people — is falling more and more under suspicion of being inherently politically incorrect, of inclining individuals toward crimethink.
Gabe: the Wikipedia page on Lindley's paradox is awful.
In the example given (as in all examples I can think of) you have the typical case that given enough examples any null hypothesis of the type heta=X can be rejected, assuming that x comes from a continuous probability distribution, with finite probability density at any point, and consequently zero probability at any point Y.
Now the "Bayesian model" using a "weakly informative prior distribution" assumes the ridiculous prior point probability of p=0.5 at the point heta=0.5, which as far as I understand gives infinite probability density. Obviously, given this (to me) extremely strange prior distribution, the Bayesian result "confirms" the null hypothesis.
I haven't had the time yet to look at the original article, but have looked at the first page of Glenn Shafer's paper (the only page that is freely available). It seems to me that the "paradox" comes from having a very strange prior distribution that gives non-zero probability to one specific point (the null hypothesis), contrary to my intuition and to what I've read so far about prior distributions. Yet Shafer claims that this is the recommended way to do it. Is there some example where such a prior distribution would make sense (intuitively)?
Radford: To call Andrew's reference "literary" is a bit of a stretch.
Jens: I agree with you completely.