The book serves a nice intro to Bayes theory for an absolute newbie. There is minimal math in the book. Whatever little math that’s mentioned, is accompanied by figures and text so that a newbie to this subject “gets” the basic philosophy of Bayesian inference. The book is a short one spanning 150 odd pages that can be read in a couple of hours. The introductory chapter of the book comprises few examples that repeat the key idea of Bayes. The author says that he has deliberately chosen this approach so that a reader does not miss the core idea of the Bayesian inference which is,
Bayesian inference is not guaranteed to provide the correct answer. Instead, it provides the probability that each of a number of alternative answers is true, and these can then be used to find the answer that is most probably true. In other words, it provides an informed guess.
In all the examples cited in the first chapter, there are two competing models. The likelihood of observing the data given each model is almost identical. So, how does one chose one of the two models ? Well, even without applying Bayes, it is abundantly obvious which of the two competing models one should go with. Bayes helps in formalizing the intuition and thus creates a framework that can be applied to situations where human intuition is misleading or vague. If you are coming from a frequentist world where “likelihood based inference” is the mantra, then Bayes appears to be merely a tweak where weighted likelihoods instead of plain vanilla likelihoods are used for inference.
The second chapter of the book gives a geometric intuition to a discrete joint distribution table. Ideally a discrete joint distribution table between observed data and different models is the perfect place to begin understanding the importance of Bayes. So, in that sense, the author provides the reader with some pictorial introduction before going ahead with numbers.
The third chapter starts off with a joint distribution table of 200 patients tabulated according to # of symptoms and type of disease. This table is then used to introduce likelihood function, marginal probability distribution, prior probability distribution, posterior probability distribution, maximum apriori estimate . All these terms are explained using plain English and thus serves as a perfect intro to a beginner. The other aspect that this chapter makes it clear is that it is easy to obtain probability of data given a model. The inverse problem, i.e probability of model given data, is a difficult one and it is doing inference in that aspect that makes Bayesian inference powerful.
The fourth chapter moves on to continuous distributions. The didactic method is similar to the previous chapter. A simple coin toss example is used to introduce concepts such as continuous likelihood function, Maximum likelihood estimate, sequential inference, uniform priors, reference priors, bootstrapping and various loss functions.
The fifth chapter illustrates inference in a Gaussian setting and establishes connection with the well known regression framework. The sixth chapter talks about joint distributions in a continuous setting. Somehow I felt this chapter could have been removed from the book but I guess keeping with the author’s belief that “spaced repetition is good”, the content can be justified. The last chapter talks about Frequentist vs. Bayesian wars, i.e. there are statisticians who believe in only one of them being THE right approach. Which side one takes depends on how one views “probability” as – Is probability a property of the physical world or is it a measure of how much information an observer has about that world ? Bayesians and increasingly many practitioners in a wide variety of fields have found the latter belief to be a useful guide in doing statistical inference. More so, with the availability of software and computing power to do Bayesian inference, statisticians are latching on to Bayes like never before.
The author deserves a praise for bringing out some of the main principles of Bayesian inference using just visuals and plain English. Certainly a nice intro book that can be read by any newbie to Bayes.