Sam Jessup writes:
I am writing to ask you to recommend papers, books–anything that comes to mind that might give a prospective statistician some sense of what the future holds for statistics (and statisticians). I have a liberal arts background with an emphasis in mathematics. It seems like this is an exciting time to be a statistician, but that’s just from the outside looking in. I’m curious about your perspective on the future of the discipline.
Any recommendations? My favorite is still the book, “Statistics: A Guide to the Unknown,” first edition. (I actually have a chapter in the latest (fourth) edition, but I think the first edition (from 1972, I believe) is still the best.
I think Introductory Statistics with R by Dalgaard would be pretty useful too for any beginning statistician. And of course there's the excellent Probability and Statistics text by DeGroot and Schervish.
Actually I picked up a copy of "Statistics: A Guide to the Unknown" as part of my initial migration into statistics – it almost made me turn around and leave.
My guess/recollection is it is/was more a book for those who have worked in statistics for a while than those for outside it.
K?
"The Lady Tasting Tea" by David Salsburg is a nice introduction to the historical development of statistics.
The book by Salsburg may prove entertaining, but it is full of extraordinary errors. See (e.g.) my review in Biometrics 57: 1273-1274 (2001).
Perhaps I can annoy Andrew by recommending the work of Edwin T. Jaynes – his 2003 book is good and thought-provoking, but for a shorter taste I'll go with this paper: "The well-posed problem", Foundations of Physics, 1973.
I am suggesting this as a counterpoint to the mainstream statistics literature, as something that may appeal to people who would be put off by mainstream treatments. If you prefer the flavour of this to the standard approach, you may be better off studying applied mathematics or computer science rather than statistics.
(Andrew – I've read what you have to say about Jaynes in your recent philosophy paper, but would be interested in any more detailed critiques. E.g. do you think his approach is fundamentally untenable, or do you just think that his idea of finding objective uninformative priors is unnecessary?)
Konrad:
I'm a big fan of Jaynes's approach of making very strong assumptions and then being willing to check model fit. Jaynes emphasized that when you build a strong model from first principles and then can reject the model, that this is a way of learning. I was strongly influenced by Jaynes's writing on this topic.
When you get to the specifics, the model has to depend on the context. Jaynes's models made a lot of sense for physics problems with lots of symmetries–this makes sense, thermodynamics was where he was coming from–but I don't know how I'd apply them to the sorts of social and environmental science problems that I work on. And, much as I'm a fan of Jaynes's work, I can't see reading his articles to get a sense of "the future of statistics," except to the extent that he is a cult figure who is admired by people who might be currently working in the area.
My background is mainly engineering physics and I would consider myself a huge fan of Jaynes. Reading through his work, the point he was always trying to get across is to always assume the minimal amount of information that you can get away with and then let the Principle of Maximum Entropy take care of the rest (I think this is the uniformed prior that Konrad is referring to). So if all you know is the mean of some measured value, do not assume that you know what the variance is. Then when you create a model by only varying the mean and you will see how much you can make sense of the results. If the data agrees with your model then it becomes very hard to argue against.
Of course this usually works best for highly disordered systems, which essentially covers all the areas where scientists flail away trying to apply complexity arguments. If they would just let entropy take over as the primary feature in their analysis, they could make lots of progress but then their funding would dry up when people realized our obviously the statistics drop out.
I spend most of the time blogging about environmental factors and applying these ideas here:
http://mobjectivist.blogspot.com/
So you are right that Jayes is absolutely a cult figure, because the people that buy into his stuff get pulled in deeper and deeper as the world starts making more and more sense.
Web:
I was going to respond with something sarcastic, but that wouldn't be polite. So let me just say that maybe you're right, but in the meantime I have my own problems to solve, and the recipe you give doesn't really help me out.
OK, I try to get insight wherever I can.
"I can't see reading his articles to get a sense of 'the future of statistics,'"
Sure, these are old writings, and you may be right.
The central idea is that one can strive to find the "best" answers to many statistical questions and/or derive the _unique_ consequences of one's modelling assumptions. This is in contrast to the traditional approach in statistics which says that there are many applicable tests for most situations, and one just selects arbitrarily (there's no a priori way of choosing the right test).
I don't know if Jaynes's emphasis on objectivity will be part of the future of statistics, but I sure hope so.
Konrad, I think the modeling aspects are where I place the emphasis. Its more akin to statistical mechanics than statistics, at least to me, and perhaps that is going to far afield for this thread. Sorry about that.