Link : What to Do at the Crossroads of Should and Must ? There are two paths in life: Should and Must. We arrive at this crossroads over and over again. And each time, we get to choose. Should is how others want us to show up in the world — how we’re supposed to think, what we ought to say, what we should or shouldn’t do. When we choose Should the journey is smooth, the risk is small

The paper titled, History of Application of Martingales in Survival Analysis, provides a nice narrative of the various scientists, mathematicians, events and concepts behind the wide-spread usage of martingales in Survival analysis. There are two major takeaways from this paper. One is of course the time line of all the developments in the field of survival analysis. The second takeaway from this paper is a good intuitive understanding of martingales + martingale stochastic integrals and their practical application in getting to asymptotic properties of many estimators.

As the title suggests, this book is truly a self-learning text. There is minimal math in the book, even though the subject essentially is about estimating functions(survival, hazard, cumulative hazard). I think the highlight of the book is its unique layout. Each page is divided in to two parts, the left hand side of the page runs like a pitch, whereas the right hand side of the page runs like a commentary to the pitch.

[youtube https://www.youtube.com/watch?v=rbf_TXqEY-Y?rel=0]

The following is a nice example from Michael Hardy that shows how excessive focus on unbiasedness of an estimator leads to nonsense results : A light source is at an unknown location µ somewhere in the unit disk D. A dart thrown at the disk strikes some random location U in the disk, casting a shadow at a point X on the boundary. The random variable U is uniformly distributed in the disk, i.