A First Course in Bayesian Statistical Methods

by Peter D. Hoff

A self-contained introduction to probability, exchangeability and Bayes' rule provides a theoretical understanding of the applied material.

Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves.

The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

Genres: Mathematics, Textbooks, Science

280 pages, Hardcover

First published January 1, 2009

Reviews

[A · Rating 3 out of 5]

This book could be useful to some, detailing some Bayesian topics and concepts and providing further examples of hierarchical modelling.

[Zhijing Jin · Rating 5 out of 5]

Reader-friendly intro to Bayesian Statistics.

- We can understand Bayesian statistics first from the Bayes Rule
- Benefit of using Bayes to learn p(theta | data) is good because we can get a distribution of theta. Also for p( data_output | data_input), we also get a distribution of data_outputs, which can represent "uncertainty."
- Then, the marginalization term in the Bayes Rule is really hard to calculate, so Variational Inference (using a q(theta) to model p(theta | data_input, data_output) ) is proposed.
- For Bayesian models, Gaussian Process (GP) is a very good and widely used example


Links to Machine Learning:
- Overview of what Bayesian Inference is, and how many other subjects like social science use Bayesian modeling https://www.nature.com/articles/s4358...
- Thesis that briefly introduces Bayesian Inference, and its relationship with Variational Inference, and Bayesian Neural Networks: http://mlg.eng.cam.ac.uk/yarin/thesis...
- Thesis by Kingma: "Variational Inference and Deep Learning: A New Synthesis" https://pure.uva.nl/ws/files/17891313... . This covers popular usage of Bayesian Inference in ML, including VAE, generative modeling and representation learning, inverse autoregressive flows, local reparameterization trick, etc.
- Gaussian process for machine learning: http://www.gaussianprocess.org/gpml/c...
- Course materials for Bayesian Statistics at Duke University (which is known for being super Bayesian): https://github.com/zhangry868/Bayesia...
- Python coding for Bayesian modeling: https://camdavidsonpilon.github.io/Pr...

[Kevin Doran · Rating 2 out of 5]

There is so much wrong with this book. God help you if this is the material you have for your first glimpse of Bayesian methods applied to statistics. It redeems itself slightly as I find it useful as a dense reference.

The book reads like an unfinished effort to convert lecture slides and notes into a book format. So many sections read like Powerpoint slides-short and somewhat disconnected from the surrounding material. Many of the subheadings are are quite possibly the vestiges of Powerpoint slide titles. The font, line spacing and margins all work to make the content harder to read. There is no page that collects and explains the notation used in the text, possibly because there there doesn't seem to be a strict convention. There is definitely some very loose uses of notation for which you have to guess what might have been intended.

Reading the preface is enlightening: "This book originated from a set of lecture notes for a one-quarter graduate-level course...The purpose of the course is to familiarize the students with the basic concepts of Bayesian theory and to quickly get them performing their own data analysis..." So yea, if you want to read lecture notes from a short course which you aren't actually taking whose purpose is to quickly get students plugging in numbers to different equations for which you probably haven't developed an intuition for yet, then this is the book for you!"

Disclaimer
I have only read about 4 chapters of the book; however, there are so many issues that I can't imagine the rest of the book managing to redeem itself.

[Leandro Carísio · Rating 3 out of 5]

As for a book titled "first course...", I imagined it would be an introduction to Bayesian statistics. However, I was mistaken: the book is far from suitable for a first encounter with the subject. For an initial introduction, "Statistical Rethinking" is a much better book.

Unfortunately, I was only able to follow the reasoning for the first half of the book (chapters 1 to 6). I was only able to extract very general concepts from chapters 7 to 12.

The book has some R code that is somewhat thrown in, not very helpful.
I recommend it for those who already know a lot about the subject, but if the idea is an introduction to Bayesian statistics, run!

[Michael Corley · Rating 3 out of 5]

I'm still searching for a readable Baysian statistics reference. I bought the digital version thinking that I would be able to use it as a reference, but it appears that it is not my ideal reference book. It is difficult to read and equally difficult to look things up in this book.

[Denis Kotnik · Rating 3 out of 5]

It was long ago when I have read this book. It was very nice introduction with a lot of exercises. But I remember there was a lot of mistakes in it, even in the equations. I think the author have a list of those on his website.

[Teodora Petkova · Rating 4 out of 5]

This textbook is a great introduction to Bayesian stats for undergraduate students. All concepts are explained thoroughly through examples, and a simplicity of the explanations is carried through the entire book.

[Paidamoyo · Rating 4 out of 5]

Great, introduction to Bayesian analysis and R.