Bayes' Rule: A Tutorial Introduction to Bayesian Analysis

The book does a good job of explaining Bayes' rule but not in a starkly different way than other books on the subject. That said, its use of graphs/plots helps visually understand Bayes' rule; animated plots would have made the explanation even more accessible. As the book moves to topics such as estimation using Bayes' rule, the exposition gets a bit dry and inaccessible.

Here's an anecdote that illustrates something the effect this book had on me: There are these two young fish swimming along, and they happen to meet an older fish swimming the other way, who nods at them and says, “Morning, boys, how's the water?” And the two young fish swim on for a bit, and then eventually one of them looks over at the other and goes, “What the hell is water?”Through reading this book, I really came to understand the extent to which maximum likelihood estimation is the 'water' of many data analysis and statistics professionals and that there is a credible alternative to this paradigm. This book is an excellent introduction to the Bayesian approach and is very accessible for readers who come from thoroughly frequentist backgrounds.

While a breezy read, I didn't find this volume as helpful as other similar ones. I certainly wouldn't consider this to be a textbook on Bayes, except for a partial course in the area. Perhaps as a starter volume, where it would suffice. I only needed a few hours to work completely through this one, though I readily admit I didn't download the supporting code and work with that.There are several errors, mostly smaller typos, but a few that took me aback and lowered my expectations. I realize the author was simplifying in many situations, but making the simple statement that ratios represent all the possible real values was a bit distracting. (That may be more on me than on Dr. Stone; nevertheless...) In all, it appears the book was rushed into production, just a bit. I also would have preferred a Kindle edition.I will admit, this book fills a niche between the popular reads on Bayesian inference and the more weighty texts. It is suitable for a beginner in Bayesian inference, especially if otherwise mathematically sophisticated and looking for a self-teaching path.

I enjoyed this book a lot. I think it is an ideal primer for more advanced texts.In more detail - I have a strong math background, but was finding advanced texts on Statistical Inference and Machine Learning (like Bishop's book) difficult to follow because they assume strong familiarity with Baye's Rule. It turns out that there are a lot of variations and ramifications around it (no doubt because it has been around a long time) and knowledge of these are assumed, but usually not covered in other texts I have looked at. This book really dealt with the whole thing, I found Chapter 3 (illustrating with a joint probability example), and 4 and 5 (showing how it can be used to solve estimations problems) particularly enlightening. It brevity also makes it easy to tackle.I do wish there were some problems to go with it. Still looking for a Bayesian Problem Book :)

Note: I've only read two chapters. I will update this review if the book improves.The author used convoluted, and sometimes wrong examples to explain Bayes rule.Chapter 2 - From the book:- Theres a bag of 100 coins- 25 Have a bias of 0.9- 75 Have a bias of 0.1(bias is probability of landing on heads)- I draw one coin. I have a 25% chance to draw a coin with 0.9 bias, and 75% chance to draw a coin with 0.1 bias.- The coin is replaced and a new coin is chosen and tossed, without knowing the bias- The book says the probability of drawing a coin of bias 0.9, replacing, and drawing and tossing a second, unknown bias coin and getting heads is 0.225.WRONG. That is the probability of drawing a 0.9 bias coin AND flipping that coin and getting heads:- 0.9 * 0.25 = 0.225 = 22.5%The probability of drawing a coin of bias 0.9 and then tossing an unknown bias coin and getting heads is:0.075 = 0.25 * 0.30.- Where 0.25 is the chance of drawing a coin of bias 0.9- And 0.30 is the chance of getting heads from a random draw and toss- 0.30 = (0.25 * 0.9) + (0.75 * 0.1)- Where 0.25 and 0.75 are probabilities of drawing one of the biased coins, and 0.9 and 0.1 are the chances of getting heads with those two coinsMaybe I was spoiled by "Statistics, 4th Edition" by Freedman, which was lucid and very well written. Dont waste your money.

This is an excellent introductory text on Bayesian analysis. The level is advanced enough that one will learn the concepts well, from the vantage point of examples and discussions that are well developed. It makes no attempt at being comprehensive or overly formal. Instead, it presents the concepts, using topics/scenarios that are developed in a way that gets the concepts and terminology in place. Armed with these, the reader should be in a position to begin a more rigorous in depth study. It is a great place to start, especially if you have little or no formal training in mathematical statistics.

Author uses simple examples to illustrate Bayes theorem applied to both discrete and continuous probabilities and clearly explain the underlying logic. Highly accessible to someone with high school algebra and calculus knowledge. Explanation of terms some books take for granted as well as the last chapter on ‘Bayesian Wars’ makes this an ideal starting point for a more advanced book.

Until recently, many texts on Bayesian inference assumed the reader had a strong background in mathematics or statistics. I found that really frustrating and it really got in my way of understanding this stuff. But this concise book (~160 pages) is a really great introduction. If I had this book when I was learning, then my journey would have been much easier.Rather than diving directly into things, Chapter 1 provides a range of examples that demonstrate some of the core concepts. I think this is really important because often people are coming from a frequentist background, and unless certain key conceptual shifts are made, then it's tricky to gain traction. Chapter 7 (Bayesian Wars) deals with this aspect as well, so I felt it might be better coming after Chapter 1.I think the topic coverage is great for an introductory book. It will get the reader familiar with the workings of a lot of basic problems/models, which provides an excellent foundation for going on to more elaborate situations such as hierarchical inference or model comparison.The inclusion of an Appendix of mathematical notation was very useful.Highly recommended. One of the best introductions to the nuts and bolts of Bayesian inference for non-statisticians.I'll make some humble suggestions for improvement if a second edition were to emerge:1. While the book does include some Matlab code, it might be worth including more snippets of code in the book (or even just in Appendices). When it boils down to it, people will be coding up the maths, and readers are likely to have a degree of programming experience. Including code snippets alongside the maths may help bridge the gulf between mathematical understanding and Matlab implementation.2. The section on Forward and inverse probability is key, and could be fleshed out with more examples (with no maths) just to give the reader a greater intuition of how this can apply in their particular domain of interest.3. Graphical model notation is becoming a very popular way of portraying probabilistic models in the literature. For me, their visual nature really helped my intuitive understanding and helped solidify concepts of generative models and inference. Figures such a 1.10 are great and do this job, but perhaps a more ubiquitous use of graphical model diagrams would help readers.

Very clear and exceptionally well written introduction to the subject with easy to follow examples and a logical sequence. Nice discussion at the end explaining the emotion and prejudice that once dogged this theory, which is fully covered in Sharon Bertsch McGrayne's complementary book, The theory that would not die, which doesn't do the maths very well. A big thank you James Stone.

Well done! Not the lightest of reading, but certainly one of the most accessible. A very informative piece of writing on a subject that, with a good exposition (as is found here), can prove to be genuinely interesting and a stimulus to further investigation --- a refreshing contrast to some pretty impenetrable texts! Would certainly recommend this book.

This book is amazing. Im a msc student in econometrics currently writting my thesis on bayesian statistics and before i started i read this book just to refresh my knowledge. It was an amazing read, very intuitive and easy to follow. Even tho i already covered all the topics of the book in some class before, i felt that there were somethings that i only completed whose intuition i only got with this book. I recommend it to every one from the beginner in bayesian statistics to the expert! My tutor (a phd in statistics, and a bayesian) told me that this author is very good and also that the book is very accurate

Very good introduction, easy to follow, explains the concepts in a simple systematic way. Obviously paying close to 20 pounds for 130 pages of text (this is the number if you exclude appendices) is a very high price, but if you are looking somewhere to start with Bayes, this is quite possibly the place.