We have seen the word “bipartisan” often during the election and during the on-going recession period. Sometimes, I think that the bipartisanship is not driven by politicians but it’s driven by media, commentator, and interpreters.

me: Why Bayesian methods?
astronomers: Because Bayesian is robust. Because frequentist method is not robust.

By intention, I made the conversation short. Obviously, I didn’t ask all astronomers the same question and therefore, this conversation does not reflect the opinion of all astronomers. Nevertheless, this summarizes what I felt at CfA.

I was educated in frequentist school which I didn’t realize before I come to CfA. Although I didn’t take their courses, there were a few Bayesian professors (I took two but it’s nothing to do with this bipartisanship. Contents were just foundations of statistics). However, I found that getting ideas and learning brilliant algorithms by Bayesians were equally joyful as learning mature statistical theories from frequentists.

How come astronomers possess the idea that Bayesian statistics is robust and frequentist is not? Do they think that the celebrated Gaussian distribution and almighty chi-square methods compose the whole frequentist world? (Please, note that F-test, LRT, K-S test, PCA take little fraction of astronomers’ statistics other than chi-square methods according to astronomical publications, let alone Bayesian methods but no statistics can compete with chi-square methods in astronomy.) Is this why they think frequentist methods are not robust? The longer history is, the more flaws one finds so that no one expect chi-square stuffs are universal panacea. Applying the chi-square looks like growing numbers of epicycles. From the history, finding shortcomings makes us move forward, evolve, invent, change paradigms, etc., instead of saying that chi-square (frequentist) methods are not robust. I don’t think we spent time to learn chi-square stuffs from class. There are too many robust statistics that frequentists have developed. Text books have “robust statistics” in their titles are most likely written by frequentists. Did astronomers check text books and journals before saying frequentists methods are not robust? I’m curious how this bipartisanship, especially that one party is favored and the other is despised but blindly utilized in data analysis, has developed (Probably I should feel relieved about no statistics dictatorship in the astronomical society and exuberant about the efforts of balancing between two parties from a small number of scientists).

Although I think more likely in a frequentist way, I don’t object Bayesian. It’s nothing different from learning mother tongues and cultures. Often times I feel excited how Bayesian get over some troubles that frequentists couldn’t.. If I exaggerate, finding what frequentists achieved but Bayesians haven’t yet or the other way around is similar to the event that by changing the paradigm from the geocentric universe to the heliocentric one could explain the motions of planets with simplicity instead of adding more numbers of epicycles and complicating the description of motions. I equally cherish results from both statistical cultures. Satisfying the simplicity and the fundamental laws including probability theories, is the most important in pursuing proper applications of statistics, not the bipartisanship.

My next post will be about “Robust Statistics” to rectify the notion of robustness that I acquired from CfA. I’d like to hear your, astronomer and statistician alike, thoughts on robustness associated with your statistical culture of choice. I only can write about robustness based what I read and was taught. This also can be biased. Perhaps, other statisticians advocate the astronomer’s notion that Bayesian is robust and frequentist is not. Not much communications with statisticians makes me difficult to obtain the general consensus. Equally likely, I don’t know every astronomer’s thoughts on robustness. Nonetheless, I felt the notion of robustness is different between statisticians and astronomers and this could generate some discussions.

I may sound like Joe Liberman, overall. But remember that tossing him one party to the other back and forth was done by media explicitly. People can be opinionated but I’m sure he pursued his best interests regardless of parties.

  1. TomLoredo:

    Hyunsook summarized her encounters with astronomers who favor Bayesian procedures:

    me: Why Bayesian methods?
    astronomers: Because Bayesian is robust. Because frequentist method is not robust.

    Hyunsook, before you spend too much time with future posts addressing this, I thought I’d chime in by noting (1) I have never heard “robustness” used as a prime motivation for a Bayesian approach; (2) I have never offered that motivation myself. I don’t know who you’ve been speaking with about this, but I suspect there is a misunderstanding on one or the other side of the conversations (perhaps about Bayesian statistics, or about the statistical meaning of “robust”).

    For what it’s worth, a few years ago, on the occasion of a review talk for an interdisciplinary gathering of astronomers, statisticians, and philosophers of science, I did a quick and informal survey of a dozen or so astronomers who have prominently featured Bayesian methods in their work, asking them why they adopted the Bayesian approach. Not a single respondent using the word “robust.” Overarching themes to their responses included: (1) Bayesian methods more directly answered their actual scientific questions or more straightforwardly addressed their problems, (2) conceptual/philosophical soundness or simplicity in terms of foundations, (3) teaching experience (physics students find frequentist reasoning confusing), (4) a level of trust in domain-specific scientific intuition, and wanting to reason as directly and explicitly as possible from that intuition. (This latter motivation, expounded at length by one respondent, is almost the opposite of robustness.) There were also numerous more technical motivations given, such as needing to straightforwardly combine disparate sources of information, or needing to handle nuisance parameters in complex settings.

    I do think robustness is an interesting issue in itself (and one that, narrowly defined, could well be used to motivate a frequentist approach to some problems), but I don’t think you’ll find robustness to be the primary motivation for Bayesian approaches in astronomy.

    12-16-2008, 5:46 pm
  2. Alex:

    I have seen “robustness” brought up in conversations about Bayesian methods in astronomy. However, in such cases, the robustness typically comes from some features of the underlying probability model, not the Bayesian nature of the analysis. For example, when modeling luminosities, the use of fatter tailed distribution (say, a power law or even a log-normal) often serves to make inferences more robust to than inclusion of very bright sources than traditional least-squares methods. So, in my experience at least, it has really been a matter of getting a better, highly structured model for the phenomenon in place. These models are typically well-suited to Bayesian inference methods, but it is essentially a separate issue.

    12-18-2008, 1:09 am
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