- 28 November: (10 – 12 noon): Mayo: On Birnbaum’s argument for the Likelihood Principle: A 50-year old error and its influence on statistical foundations (See my blog and links within.)
5 December and 12 December: Statistical Science meets philosophy of science: Mayo and guests:
- 5 Dec: 12 (noon)- 2p.m.: Sir David Cox
- 12 Dec (10-12).Dr. Stephen Senn;
Dr. Christian Hennig: TBA
Topics, activities, readings :TBA (Two 2012 Summer Seminars may be found here).
Blurb: Debates over the philosophical foundations of statistical science have a long and fascinating history marked by deep and passionate controversies that intertwine with fundamental notions of the nature of statistical inference and the role of probabilistic concepts in inductive learning. Progress in resolving decades-old controversies which still shake the foundations of statistics, demands both philosophical and technical acumen, but gaining entry into the current state of play requires a roadmap that zeroes in on core themes and current standpoints. While the seminar will attempt to minimize technical details, it will be important to clarify key notions to fully contribute to the debates. Relevance for general philosophical problems will be emphasized. Because the contexts in which statistical methods are most needed are ones that compel us to be most aware of strategies scientists use to cope with threats to reliability, considering the nature of statistical method in the collection, modeling, and analysis of data is an effective way to articulate and warrant general principles of evidence and inference.
Room 2.06 Lakatos Building; Centre for Philosophy of Natural and Social Science London School of Economics Houghton Street London WC2A 2AE
Administrator: T. R. Chivers@lse.ac.uk
For updates, details, and associated readings: please check the LSE Ph500 page on my blog or write to me.
*It is not necessary to have attended the 2 sessions held during the summer of 2012.
All: I learned that the T building at the LSE is back being called the Lakatos building as it used to be, and the room number has a dot following the 2: Lak 2.06.
I was looking at your paper “Error Statistics” and ran into a problem I hoped you or Dr. Spanos could help me with. Throughout the paper there is the example SEV(mu>mu1) which is calculated by P(d(X)<d(x0);mu=mu1). It’s a great example and I love how it puts to rest so many of the howlers thown against Frequentist Statistics. Using the SEV does seem to eliminate many, if not, all the problems for Frequentists.
The problem I’m having is that by a simple change of variables it’s easy to show P(d(X)mu1|d(x0)) (for a uniform prior on mu). This is exactly the natural quantity a Bayesian would want to use to evaluate the hypothesis mu>mu1. This is a simple change of variables (essentially: d(X) equal to d(x0)+mu1-mu, where d(X) and mu are integration variables) and holds for any constants d(x0), mu1; so please don’t dismiss my concern.
Given this numerical identity, then all the great arguments for how SEV solves the problems of Frequentist Statistics apply just as easily for the Bayesian calculation (at least in this example). This can’t possibly be right, so I wanted to find an example that clearly showed the superiority of SEV.
Since the Bayesian result depended on a uniform prior for mu, what happens when we have prior knowledge that mu lies within a certain range [a,b]? The Bayesian could then restrict their uniform prior for mu to this interval. To show the Bayesians up I wanted to get the equivalent SEV answer, but I’m having a lot of trouble.
From you I learned that the only philosophically sound way to take prior knowledge into consideration is by changing the model and not with a prior probability, but how do I do that in this case? The prior knowledge has no effect on the sampling distribution at all. The error distribution just comes from a “well calibrated measuring instrument” and isn’t changed by information I have on the thing I’m measuring.
I’m tempted to just throw this prior info away and say it has no effect on the numerical value of SEV, but that can’t be right either. In an extreme case the prior info could be so restrictive that we know for certain mu>mu1. The Bayesian result will handle this extreme case perfectly, but SEV won’t unless it too somehow includes this information.
So can you or Dr. Spanos tell me how to change the sampling distribution to include the knowledge that mu is in [a,b] and how to show that the resulting SEV has much better properties than the equivalent Bayesian calculation?