Title: Statistical Models: Theory and Practice (click for the publisher’s website)
My one line review, rather a comment several months ago was

Bias in asymptotic standard errors is not a familiar topic for astronomers

and I don’t understand why I wrote it but I think I came up this comment owing to my pursuit of modeling measurement errors occurring in astronomical researches.

My overall impression of the book was that astronomers might not fancy it because of the cited examples and models quite irrelevant to astronomy. On the contrary, I liked it because it reflects what statistics ought to be in the real data analysis world. This does not mean the book covers every bit of statistics. When you teach statistics, you don’t expect student’s learning curve of statistical logistics is continuous. You only hope that they jump the discontinuity points successfully and you give every effort to lower the steps of these discontinuity points. The book looked to offering comforts to ease such efforts or to hint promises for almost continuous learning curves. The perspective and scope of the book was very impressive to me at that time.

It is sad to learn brilliant minded people passing away before their insights reach others who need them. I admire professors at Berkeley, not only because of their research activities and contributions but also because of their pedagogical contributions to statistics and its applications to many fields including astronomy (J. Neyman and E. Scott. are as familiar to statisticians as to astronomers, for example. Their papers about the spatial distribution of galaxies are, to my knowledge, well sought among astronomers).

On the likelihood ratio for source identification by Sutherland and Saunders (1992) in MNRAS vol. 259, pp. 413-420.

Their computed likelihood ratio (L) correspond to Bayes factor by the form (P(source model)/P(background model)). Considering the fact that it’s binary, source or background, L shares the form of a hazard ratio (L=p(source)/p(not source)=p(source)/(1-p(source)). Since the likelihood can be based on probability density function, the authors defined “Likelihood ratio” literally by taking the ratio of two likelihood functions. Not taking the statistical direction as in the likelihood ratio test and the Neyman-Pearson lemma, naming their method as “likelihood ratio technique” seems proper, and it’s not derogatory any more. The focus of the paper is that estimating the probability density functions of backgrounds and sources more or less empirically without concerns toward general statistical inference. Hitherto, the large Bayes factor, large L (likelihood ratio) of a source, or large posterior probability of a source (p(genuine|m,c,x,y)=L/(1+L)) is just an indicator that the given source is more likely a real source.

In summary, the likelihoods of source and of background (of numerator and of denominator) are empirically obtained based on physics which turned out to have matching parametric distributions well discussed in statistics. What is different from statistics is that the likelihood ratio didn’t lead to testing hypothesis based on Neyman-Pearson Lemma. Computing the likelihood ratio is utilized as an indicator of a source. Well, often times, it’s hard to judge the real content of an astronomical study by its name, title, or abstract due to my statistically oriented stereotypes.