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).

He started his professional life as a probabilist and mathematical statistician with Bayesian leanings but became one of the world’s leading applied statisticians and a circumspect frequentist. In his words:

My own experience suggests that neither decision-makers nor their statisticians do in fact have prior probabilities. A large part of Bayesian statistics is about what you would do if you had a prior. For the rest, statisticians make up priors that are mathematically convenient or attractive. Once used, priors become familiar; therefore, they come to be accepted as ‘natural’ and are liable to be used again; such priors may eventually generate their own technical literature… Similarly, a large part of [frequentist] statistics is about what you would do if you had a model; and all of us spend enormous amounts of energy finding out what would happen if the data kept pouring in.

I have draft posts: one is about his book titled as Statistical Models: Theory and Practice and the other is about his article appeared in arXiv:stat not many months ago and now published in the American Statistician (TAS). In my opinion, both would help astronomers lowering the barrier of theoretical statistics, Bayesian and frequentist methods alike. I blame myself for delaying these posts. Carrying on one’s legacy, I believe, is easier while the person is alive.

Survival Analysis: A Primer by David A. Freedman
The American Statistician, May 2008, Vol. 62, No.2, pp. 110-119

This article explains the basics of survival analysis and adds criticisms on previously conducted studies. Since the given examples are from medical studies, astronomers may not be interested in reading the whole article. Nonetheless, Freedman offers the definitions in survival analysis such as survival function, hazard rate, the Kaplan-Meier estimator, the proportional hazard model with clarity and conciseness. For example, if τ (a positive random variable indicating the waiting time for failure) is Weibull, the hazard rate takes an exact form of the celebrated power law in astronomy (I think modification of pdfs reflecting censoring and truncation may lead more robust results compared to fitting power laws unless parameters in power laws have astrophysical implications and survival analysis approaches cannot perform the same parametrization).

Commonality between power laws and Pareto distributions and frequent appearance of power laws in astronomical journals drives some anticipation of frequent applications of survival analysis to astronomical data; on the contrary, there are not many.

Though there are more, here are a few references relevant to survival analysis, that utilized examples from astronomy or appeared astronomical journals:

• Nonparametric Methods for Doubly Truncated Data by B Efron and V Petrosian. (subscription required)
  Journal of the American Statistical Association, Vol. 94, pp. 824-834 (1999)
• Survival Analysis of the Gamma-Ray Burst Data by B Efron and V Petrosian. (subscription required)
  Journal of the American Statistical Association, Vol. 89, pp. 452-464 (1994)
• A simple test of independence for truncated data with applications to redshift surveys by B Efron and V Petrosian
  ApJ, Vol. 399, pp.345-352 (1992)
• Statistical methods for astronomical data with upper limits. I – Univariate distributions by Feigelson and Nelson
  ApJ, Vol. 293, pp.192-206 (1985)
• Nonparametric Estimation of the Slope of a Truncated Regression by Bhattacharya, Chernoff, and Yang (subscription required)
  The Annals of Statistics, Vol. 11(2), pp. 505-514 (1983)

Note that these papers only dealt particular statistical interests with an general introduction about survival analysis and definitions of estimators based on relatively small sample size data sets. Facing massive survey data with truncation and heterogeneity in measurement errors in astronomy could open a new era of survival analysis.

Lastly, there are studies regarding Pareto distribution some of which are presented in the slog. (Use “search” with Pareto. More statistical papers on survival analysis in astronomy are welcome to be added; please, inform me.)