Dr Fisher's casebook

At my first successful interview for a lecturing post, a learned consultant asked: "What is the purpose of teaching medical students statistics?" He obviously doubted the necessity, but had to sit on the appointments panel since the medical faculty has stumped up the money. I replied rather sanctimoniously: "So that patients receive better care" It may not have been Descartes but it got me the job, and I have never stopped believing it.     

Dr Fisher's casebook

Regression to the mean is a classic statistical paradox and is a rare opportunity for statisticians to illustrate our uses to the general public.     

Dr Fisher's casebook: In praise of simple methods

An electrician was called out to fix a faulty piece of electrical equipment. He looked at it carefully and then produced his hammer and hit the machine very precisely. It then worked and for this he charged £100. When the customer protested that this was very expensive for such a simple procedure, the electrician wrote him an itemised bill.     

Dr Fisher’s casebook

Life as a jobbing statistician in a medical school bears a strong resemblance to life as a general practitioner: you have to be a jack-of-all-trades, you hold clinics where all the great unwashed can come, unfiltered and uneducated, and you get patronised by the consultants.     

Dr Fisher’s casebook

Over the years I have been consulted by many people on aspects of their research. Many were just the one brief encounter; they never came back and I never heard whether my advice had been heeded. As I say now to junior colleagues: " You have to kiss a lot of frogs before you meet a prince" .     

Penalized classification using Fisher's linear discriminant

We consider the supervised classification setting, in which the data consist of p features measured on n observations, each of which belongs to one of K classes. Linear discriminant analysis (LDA) is a classical method for this problem. However, in the high-dimensional setting where p ? n, LDA is not appropriate for two reasons. First, the standard estimate for the within-class covariance matrix is singular, and so the usual discriminant rule cannot be applied. Second, when p is large, it is difficult to interpret the classification rule obtained from LDA, since it involves all p features. We propose penalized LDA, a general approach for penalizing the discriminant vectors in Fisher's discriminant problem in a way that leads to greater interpretability. The discriminant problem is not convex, so we use a minorization-maximization approach in order to efficiently optimize it when convex penalties are applied to the discriminant vectors. In particular, we consider the use of L(1) and fused lasso penalties. Our proposal is equivalent to recasting Fisher's discriminant problem as a biconvex problem. We evaluate the performances of the resulting methods on a simulation study, and on three gene expression data sets. We also survey past methods for extending LDA to the high-dimensional setting, and explore their relationships with our proposal.