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.

The problem with data analysis is of course that it is a performing art. It is not something you easily write a paper on; rather, it is something you do. And so it is difficult to publish.

quoted from this conversation ——————————————————-

Statistical Science has a nice “conversations” series with renown statisticians. This series always benefits me because of 1. learning the history of statistics through a personal life, 2. confronting various aspects in statistics as many statisticians as were interviewed, and 3. acquiring an introductory education in the statistics that those interviewees have perfected over many years in a plain language. One post in the slog from this series was a conversation with Leo Breiman about the two cultures in statistical modeling. Because of Prof. Huber’s diverse experiences and many contributions in various fields, this conversation may entertain astronomers and computer scientists as well as statisticians.

The dialog is available through arxiv.org: [stat.ME:0808.0777] written by Andreas Buja, Hans R. Künsch.

He became famous due to his early year paper in robust statistics titled, Robust Estimation of a Location Parameter but I see him as a pioneer in data mining, laying a corner stone for massive/multivariate data analysis when computers were not as much capable as today’s. His book, Robust Statistics (Amazon link) and the paper Projection Pursuit in Annals of Statistics (Vol. 13, No. 2, pp. 435-475, yr. 1985) are popular among many well known publications.

He has publications in geoscience and Babylonian astronomy. This conversation includes names like Steven Weinberg, the novel laureate (The First Three Minutes is a well known general science book) and late Carl Sagan (famous for books/a movie like Cosmos and Contact) showing his extent scholarly interests and genius beyond statistics. At the beginning, I felt like learning the history of computation and data analysis apart from statistics.