Once I tried to understand ARF, RMF, PSF in X-ray observations from the ANOVA perspective. For example, one’s best fit depends on a source model within which ARF is nested. I wanted to see ARF as random effect but was not sure how things were crossed. Overall, the nested structure was not clear to me. If the structure becomes clear, I guess Bayesian modeling is naturally incorporated for fitting (factoring statistical and systematical uncertainties as by product) and testing source models (Bayes factor instead of goodness of fits).

It is a very good read (Gelman is a very good writer and speaker) but I’m afraid how many astronomers will bother to learn ANOVA and related statistics. The lexicons in design of experiments and consequent statistical inference seem very absurd for astronomers, at least I felt that way when I just began to learn statistics.

]]>The nicest overview of ANOVA I’ve come across is a lovely article by Andrew Gelman from *Annals of Statistics* in 2005: Analysis of variance–why it is more important than ever. I especially like the connections it makes between ANOVA and hierarchical (multilevel) modeling and regression, and the Bayesian flavor Gelman gives to ANOVA (normally considered frequentist territory) I think will appeal to a physical scientist’s intuition more than the treatments in stats texts.