I want to shift to the arena of testing the adequacy of statistical models and misspecification testing (leading up to articles by Aris Spanos, Andrew Gelman, and David Hendry). But first, a couple of informal, philosophical mini-posts, if only to clarify terms we will need (each has a mini test at the end). Continue reading Monthly Archives: January 2012
No-Pain Philosophy: Skepticism, Rationality, Popper, and All That: First of 3 Parts
I want to shift to the arena of testing the adequacy of statistical models and misspecification testing (leading up to articles by Aris Spanos, Andrew Gelman, and David Hendry). But first, a couple of informal, philosophical mini-posts, if only to clarify terms we will need (each has a mini test at the end). Continue reading Updating & Downdating: One of the Pieces to Pick up on
pieces to pick up on (later)
Before moving on to a couple of rather different areas, there’s an issue that, while mentioned by both Senn and Gelman, did not come up for discussion; so let me just note it here as one of the pieces to pick up on later.
“It is hard to see what exactly a Bayesian statistician is doing when interacting with a client. There is an initial period in which the subjective beliefs of the client are established. These prior probabilities are taken to be valuable enough to be incorporated in subsequent calculation. However, in subsequent steps the client is not trusted to reason. The reasoning is carried out by the statistician. As an exercise in mathematics it is not superior to showing the client the data, eliciting a posterior distribution and then calculating the prior distribution; as an exercise in inference Bayesian updating does not appear to have greater claims than ‘downdating’ and indeed sometimes this point is made by Bayesians when discussing what their theory implies. (59)…..” Stephen Senn
“As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior.” Andrew Gelman commenting on Senn
I’ve even heard subjective Bayesians concur on essentially this identical point, but I would think that many would take issue with it…no?
Categories: Statistics
Tags: Andrew Gelman, Bayesian, downdating and updating, Stephen Senn
U-PHIL (3): Stephen Senn on Stephen Senn!
I am grateful to Deborah Mayo for having highlighted my recent piece. I am not sure that it deserves the attention it is receiving.Deborah has spotted a flaw in my discussion of pragmatic Bayesianism. In praising the use of background knowledge I can neither be talking about automatic Bayesianism nor about subjective Bayesianism. It is clear that background knowledge ought not generally to lead to uninformative priors (whatever they might be) and so is not really what objective Bayesianism is about. On the other hand all subjective Bayesians care about is coherence and it is easy to produce examples where Bayesians quite logically will react differently to evidence, so what exactly is ‘background knowledge’?. Continue reading
Categories: Philosophy of Statistics, Statistics, U-Phil
Tags: Bayesianism, cross-over trials, Stephen Senn
U-PHIL: Stephen Senn (2): Andrew Gelman
I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize “my” Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are!
Categories: Philosophy of Statistics, Statistics, U-Phil
Tags: Carlin, de Finetti, Gelman, Rubin, Senn
U-PHIL: Stephen Senn (1): C. Robert, A. Jaffe, and Mayo (brief remarks)
I very much appreciate C. Robert and A. Jaffe sharing some reflections on Stephen Senn’s article for this blog, especially as I have only met these two statisticians recently, at different conferences. My only wish is that they had taken a bit more seriously my request to “hold (a portion of) the text at ‘arm’s length,’ as it were. Cycle around it, slowly. Give it a generous interpretation, then cycle around it again self-critically” (January 13, 2011). (I conceded it would feel foreign, but I strongly recommend it!)Since these authors have given bloglinks, I’ll just note them here and give a few brief responses:
Categories: Philosophy of Statistics, Statistics, U-Phil
Tags: A. Jaffe, C. Robert, Jaynes, S. Senn
RMM-6: Special Volume on Stat Sci Meets Phil Sci
The article “The Renegade Subjectivist: José Bernardo’s Reference Bayesianism” by Jan Sprenger has now been published in our special volume of the on-line journal, Rationality, Markets, and Morals (Special Topic: Statistical Science and Philosophy of Science: Where Do/Should They Meet?)
Abstract: This article motivates and discusses José Bernardo’s attempt to reconcile the subjective Bayesian framework with a need for objective scientific inference, leading to a special kind of objective Bayesianism, namely reference Bayesianism. We elucidate principal ideas and foundational implications of Bernardo’s approach, with particular attention to the classical problem of testing a precise null hypothesis against an unspecified alternative.
Categories: Philosophy of Statistics, Statistics
Tags: Bernardo, Jan Sprenger, RMM
"Philosophy of Statistics": Nelder on Lindley
A friend from Elba surprised me by sending the interesting paper and discussion of Dennis Lindley (2000), “The Philosophy of Statistics,” which I hadn’t seen in years. She suggested, as especially apt, J. Nelder’s remarks; I recommend the full article and discussion:
(from) Comments by J. Nelder:
Recently (Nelder,1999) I have argued that statistics should be called statistical science, and that probability theory should be called statistical mathematics (not mathematical statistics). I think that Professor Lindley’s paper should be called the philosophy of statistical mathematics, and within it there is little that I disagree with. However, my interest is in the philosophy of statistical science, which I regard as different. Statistical science is not just about the study of uncertainty but rather deals with inferences about scientific theories from uncertain data. Continue reading
Categories: Statistics
Tags: Dennis V. Lindley, error statistical philosophy, J. Nelder
Mayo Philosophizes on Stephen Senn: "How Can We Cultivate Senn’s-Ability?"
Where’s Mayo?
Although, in one sense, Senn’s remarks echo the passage of Jim Berger’s that we deconstructed a few weeks ago, Senn at the same time seems to reach an opposite conclusion. He points out how, in practice, people who claim to have carried out a (subjective) Bayesian analysis have actually done something very different—but that then they heap credit on the Bayesian ideal. (See also the blog post “Who Is Doing the Work?”) Continue reading
“You May Believe You Are a Bayesian But You Are Probably Wrong”
The following is an extract (58-63) from the contribution by
Stephen Senn (Full article)
Head of the Methodology and Statistics Group,
Competence Center for Methodology and Statistics (CCMS), Luxembourg
…..
I am not arguing that the subjective Bayesian approach is not a good one to use. I am claiming instead that the argument is false that because some ideal form of this approach to reasoning seems excellent in theory it therefore follows that in practice using this and only this approach to reasoning is the right thing to do. A very standard form of argument I do object to is the one frequently encountered in many applied Bayesian papers where the first paragraphs lauds the Bayesian approach on various grounds, in particular its ability to synthesize all sources of information, and in the rest of the paper the authors assume that because they have used the Bayesian machinery of prior distributions and Bayes theorem they have therefore done a good analysis. It is this sort of author who believes that he or she is Bayesian but in practice is wrong. (58) Continue reading
Categories: Philosophy of Statistics, Statistics
Tags: Bayesianism, Stephen Senn
U-PHIL: "So you want to do a philosophical analysis?"
“Philosophy, as I have so far understood and lived it, means living voluntarily among ice and high mountains—seeking out everything strange and questionable in existence”. Nietzsche*I am about to turn to philosophical analyses/deconstructions of short portions of articles from the special issue “Statistical Science and Philosophy of Science” (RMM 2011), and I will invite contributed analyses from readers and, of course, the author(s). The first text, to be posted tomorrow, will be from Professor Stephen Senn. (Full article)
Categories: philosophy of science, U-Phil
Tags: Nietzsche, philosophical analysis
PhilStatLaw: Bad-Faith Assertions of Conflicts of Interest?*
In response to an indication that the FDA might need to loosen conflict-of-interest (COI) rules to get sufficient experts to serve on their advisory panels, a list has been proferred of “industry-free” experts capable of serving with “clean hands” (See Oct 10 post: Junk Science ) But why not also seek “litigation-free” experts, asks lawyer, Nathan Schachtman on his interesting blog (Dec. 28) The Continuing Saga of Bad-Faith Assertions of Conflicts of Interest:
Don’t Birnbaumize that Experiment my Friend*
(A) “It is not uncommon to see statistics texts argue that in frequentist theory one is faced with the following dilemma: either to deny the appropriateness of conditioning on the precision of the tool chosen by the toss of a coin[i], or else to embrace the strong likelihood principle which entails that frequentist sampling distributions are irrelevant to inference once the data are obtained. This is a false dilemma … The ‘dilemma’ argument is therefore an illusion”. (Cox and Mayo 2010, p. 298)
Continue reading
Categories: Statistics
Tags: Birnbaum, David Cox, Likelihood Principle, Robert
Model Validation and the LP-(Long Playing Vinyl Record)
A Bayesian acquaintance writes:
Although the Birnbaum result is of primary importance for sampling theorists, I’m still interested in it because many Bayesian statisticians think that model checking violates the likelihood principle, as if this principle is a fundamental axiom of Bayesian statistics.
But this is puzzling for two reasons. First, if the LP does not preclude testing for assumptions (and he is right that it does not[i]), then why not simply explain that rather than appeal to a disproof of something that actually never precluded model testing? To take the disproof of the LP as grounds to announce: “So there! Now even Bayesians are free to test their models” would seem only to ingrain the original fallacy. Continue reading
Categories: Statistics
Tags: Jim Berger, Likelihood Principle, sampling distribution, testing model assumptions
The Statistics Wars & Their Casualties
LSE PH500 Research Seminar (May 21-June 25, 2020): Controversies in Phil Stat
Summer Seminar 2019 (article)
Experts convene to explore new philosophy of statistics field
Error Statistics Philosophy 