This book is recommended on Statistics Exchange as the book best suited for a complete beginner about Bayesian statistics: http://stats.stackexchange.com/questions/125/what-is-the-best-introductory-bayesian-statistics-textbook
Fortunately I found a pdf copy on the author's own website.
Overall, I wouldn't recommend:-
- Focussed on explaining probability theory, whereas I want to understand how to do a statistical analysis without necessarily understand the theory.
- Folksy style: "Suppose that you and a friend dine at Uncle Wong's Chinese Restaurant ..."
- Not sure if I agree with everything Briggs says, although I am a beginning student, and he is a long term professor.
- Polemical style: Briggs opinion gets in the way of clear exposition (but there is something pleasant about an academic having an opinion, and being prepared to follow it).
Comments / Observations / Quotes
1. p vii: when explaining the difference between Bayesian and Frequentist statistics:
The second difference ..... [is] to create a probability requires fixing certain mathematical objects called parameters..... these parameters do not exist, they cannot be measured, seen.... . This book will show you how to remove the influence of parameters and bring the focus back to reality, to real, tangible , measurable, observables.
2. The books The Rationality of Induction by David Stove and Probability Theory: The Logic of Science by Edwin Jaynes – "quite literally changed my entire way of thinking about uncertainty, probability and philosophy."
3. Both gambling and biological trials are situations where the relative frequencies of the events, like dice rolls and ratios of crop yields, can very quickly approach the actual probabilities. .... Since people were focussed on gambling and biology, they did not realise that some arguments that have a logical probability do not equal their relative frequency (of being true).
4. Hajek (1997) collects many examples of why frequentism fails.
5. Randomness: "there is a great deal of nonsense written and said about randomness. Although it's never stated directly, there is a certain mysticism about randomness which is supposed to "bless" statistical results. Samples must be "random" to be statistically valid, it is often said. This view is false. "
6. Randomness again : A favourite term is randomised trial, which are the only kind of experiment accepted in some quarters, all other forms of trial deemed untermenchen (tell this to physicists and chemists etc who regularly run unrandomised trials, yet have managed to learn a great deal about the world"
Briggs compares randomized trials with controlled experiments. The point Briggs seems to be missing is that in social science type experiments, you can't control for all the variables of a human.
7. Good point: Briggs introduces R in an introductory text.
8. Briggs makes the point that there are limitations with classical statistics. For example, there is a fair amount of debate about the usefulness of using p values and null hypothesis testing. And there are a lot of other issues with classical statistics, which he highlights in chapter 14: Cheating. However, the point needs to be made that these shortcomings are also being addressed within the mainstream tradition.
9. Some of the material in Briggs is probably a bit complex for a complete beginner, but that's feedback for the person who recommended the book on Statistics Exchange, not a criticism of the book itself. In particular, the chapters on Regression Modelling and Logistic Regression were a bit harder to follow. And anyway, the discussion on probability theory itself requires commitment on the part of the reader.
10. I found Briggs' comments on confidence intervals interesting
- How do classical statisticians express uncertainty about parameter? à use confidence interval
- Construct an infinite number of confidence intervals, when you are done, 95% of those intervals will cover the actual value of u.
- You cannot say there is a 95% that true value of u lies in the 95% CI I have just constructed àthere is no interpretation of your confidence interval other than: your interval either contains or does not contain true value of u.
- Your CI only has an interpretation as part of an infinite set of other CIs
As I mentioned before, my first response is to see if I can reconcile both positions.
I'm not sure if it matters if I construct a confidence interval based on one sample rather than create multiple confidence intervals based on multiple samples à sampling theory tells me something about how those infinite samples will be distributed. Yes, Briggs is correct, my confidence interval will or will not contain the true parameter value. However, sampling theory suggests that my confidence interval is likely to be closer to rather than further away.
11. I think Briggs misrepresents to some degree classical hypothesis testing. For example, when we have two means, say 421 and 440, we are not asking if they are equal, as Briggs suggests we do. Rather, we are asking if they are likely to come from the same distributions, which is the same as saying whether they both have the same generating function. The formal way of writing out the hypothesis test obscures the logic behind the test.
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