Comments on: my first AAS. III. ANOVA http://hea-www.harvard.edu/AstroStat/slog/2008/first-aas-anova/ Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 01 Jun 2012 18:47:52 +0000 hourly 1 http://wordpress.org/?v=3.4 By: hlee http://hea-www.harvard.edu/AstroStat/slog/2008/first-aas-anova/comment-page-1/#comment-266 hlee Wed, 02 Jul 2008 19:30:43 +0000 http://hea-www.harvard.edu/AstroStat/slog/?p=337#comment-266 I'm always very much obliged to have your comments! My slow reading delayed showing my gratitude, though. I never ponder on ANOVA from a Bayesian perspective. I only have a notion that it's a great way to see regressions or (generalized) linear models whose components are not necessarily ruled by physics but needs interpretations in terms of their significance in model contribution. The challeges comes in when the structures of components for mutli-way ANOVA and MANOVA. 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. I’m always very much obliged to have your comments! My slow reading delayed showing my gratitude, though. I never ponder on ANOVA from a Bayesian perspective. I only have a notion that it’s a great way to see regressions or (generalized) linear models whose components are not necessarily ruled by physics but needs interpretations in terms of their significance in model contribution. The challeges comes in when the structures of components for mutli-way ANOVA and MANOVA.

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.

]]> By: TomLoredo http://hea-www.harvard.edu/AstroStat/slog/2008/first-aas-anova/comment-page-1/#comment-260 TomLoredo Sat, 28 Jun 2008 03:29:47 +0000 http://hea-www.harvard.edu/AstroStat/slog/?p=337#comment-260 Thanks, Hyunsook, for the comments on ANOVA. Just thought I'd point out for astronomers that ANOVA is not at all limited to design of experiments. It's a kind of umbrella term for a group of methods that try to study parameters in groups (perhaps of size one), to see whether and where they are important across a set of subjects. ANOVA arises in inferential statistics as well as in experimental design and exploratory data analysis. The nicest overview of ANOVA I've come across is a lovely article by Andrew Gelman from <em>Annals of Statistics</em> in 2005: <a href="http://arxiv.org/abs/math/0504499" rel="nofollow">Analysis of variance--why it is more important than ever</a>. 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. Thanks, Hyunsook, for the comments on ANOVA. Just thought I’d point out for astronomers that ANOVA is not at all limited to design of experiments. It’s a kind of umbrella term for a group of methods that try to study parameters in groups (perhaps of size one), to see whether and where they are important across a set of subjects. ANOVA arises in inferential statistics as well as in experimental design and exploratory data analysis.

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.

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