Likelihood function is a very useful mathematical object in statistics. With it, you can perform the two main tasks in statistics,i.e. estimation and inference. If you can get the distribution right or the overall structural equation right, you can do all types of stats; univariate stats, multivariate stats , linear models, generalized linear model, mixture modeling, mixed effects model and even non parametric statistics to an extent. All of this can be done from scratch with one math object, “Likelihood function” + pen & paper + a plain vanilla optimization routine.
In these days of readily available functions and packages that do everything, often the modeler is left with a 10,000 ft. view of things only. For example, if you are doing a Poisson regression, the modeling of dispersion parameter is close to automatic in R, SAS, SPSS. It almost looks like magic. What’s going on under the hood ? If one goes to the Frequentist side of world and explore things, one often finds heavy reliance on asymptotics and heaps of formulae. If you go to the Bayesian world, there is some learning curve in terms of setting up the right infra to get to the bottom of the stuff. You need to know BUGS and also a way to invoke BUGS from your programming environment. So, sometimes back of envelope parameter estimation and inference becomes elusive. Having said that, the knowledge of Bayesian world is definitely better than living ONLY in the Frequentist world.
But there is an alternate world between this Frequentist and Bayesian mode of thinking, The Fisherian World. This is very appealing world to inhabit from time to time. In this world, all one needs to know is, just one object , “Likelihood function”. That’s it. Once you have the likelihood function for whatever data you have , estimation and inference is largely computational. What I mean by computational is, a plain vanilla optimization routine. Nothing fancy.
I like bootstrapping for, it gets me out of Frequentist world. However bootstrapping takes me only so far. If I have to find relationships between variables, hypothesize a model and test it, I have to eventually fall back to a non-bootstrapping world.
Till date, I have came across Fisherian concepts only in bits and pieces. “Maximum Likelihood estimation” is something that looked nice and easy to apply. Fisher information was convenient to get standard errors of estimates. However I made the mistake of thinking that MLE and Fisher information is all that is there in the Fisher’s world. A grave mistake. This book opened my eyes to a completely new world of modeling and inference.
Brad Efron, says in one of his papers, that 21st century stats will heavily rely on long forgotten Fisherian concepts. Whether the prediction comes true or not, learning Fisherian way of modeling and inference is going to change the way you think about many aspects of statistics.
This book is the main reason for me being thrilled about the whole Fisher’s way of thinking. The book is extremely well written and a diligent reader can reap massive benefits by spending time and effort on it. I think it is THE BEST book on statistics that I have ever read till date. When I worked through this book, it seemed like I was climbing a hillock at regular intervals, rather than a big mountain. The author introduces various concepts with a seemingly challenging problem, i.e a steep climb on a hillock and then allows you to glide smoothly down the hillock.This type of presentation does not tire the reader or create fatigue. May be stats teachers/faculty can take a cue from this book to organize their lectures for the students.
A great quote from the book ,
Understanding statistics is best achieved through a direct experience, in effect letting the knowledge pass through the fingers rather than the ears and the eyes only.
Indeed, this book makes a strong case for coding up stuff and letting the knowledge pass through fingers. Every chapter has concepts that become mightily clear, ONLY after coding. In fact there isn’t a single chapter in the book where one can merely read the contents and get the message.
Reading this book has been a delightful experience. May the best thing to have happened to me in 2012.