Likelihood

Dr Edwards' book is a real gem for anyone interested in dealing with likelihood. The Author makes an extraordinary job in finessing out subtle differences not trivial, at first sight. Statistical 'learning' is treated from different perspectives, recalling Bayesian approach and emphasizing the differences with the axiomatic likelihood approach proposed by Dr Fisher and deepened also by Dr Edwards. With sound examples the whole learning process and inference is reinterpreted (and rewritten) in the likelihood context, demonstrating the rigor, both from a logical and a mathematical point of view, and the several advantages offered by the likelihood approach when someone wants to test the validity of one hypothesis against another one (or others). Overall, I strongly recommend this book.

Owen's book "Empirical Likelihood" (2001) is the successor of the mantle of this book, and you may want to own both if you plan to do analysis in this arena. Likelihoodists are a rare little breed sitting on the fence in between Bayesians and Frequentists. There is so much muddling between the camps now that most recently graduated practicioners aren't likely (there's that word again) to draw a crisp distinction between the camps. But this volume does draw the philosophical argument out into the open, rawly. For those that say the arguments are settled, I'd say read this volume and at least absorb what it has to say. Then move on to the more updated (and more expensive) book by Owen. This book is less dogmatic than Earman's Bayes or Bust, though it does quote from Earman a fair bit. You'll appreciate the simplicity of the writing and style here, too. Edwards' last stand on this topic is worth the look.

To those who work in academic probability theory, the name of the world famous Cambridge University statistician and theoretical geneticist Ronald Fisher needs no introduction, just as true genius needs no favourable introduction by friends who knew them. To those who work in practical statistics today, the method of maximum likelihood has become something of a cliche. But it was first invented by R Fisher and was an idea of pure genius. A W Edwards was Fisher's last PhD student supervised at the famous mathematical college Caius. He has extended Fisher's work and given it a new twist - to use ideas from mathematical logic to axiomatise the method of maximum likelihood and amazingly rigorously build up a new theory of probability, different from Laplace and Kolgomorov. Please buy this book - it will give you a new perspective of probability.

Reasoning in terms of likelihoods is completely routine these days. In many areas - string matching, signal decoding, model-building - it is used without any special mention, like any other fundamental. It seems hard to remember that, not too long ago, likelihood and Bayesian techniques were the topics of impassioned debate - somtimes on different sides of the debate. This little book dates back to that era.The book addresses the use of likelihood in a number of familiar applications (parameter estimation, etc). The examples are numerous and clear. I find more recent writings to be more directly applicable, though. The real value of this book, for me, is the historical perspective that the author brings to the discussion. Early in his career, he worked with Fisher - one of the founders of modern statistics. Edwards describes how likelihood-based analysis grew out of that tradition. He also restates some of the philosophical objections to Bayesian analysis, especially questioning the use of priors. I didn't come away from this book with any new analytic skills, though I suppose I could have mined the text more deeply. I did come away impressed by how much applied math and probability modeling have changed just since the 70s.