http://www.stat.auckland.ac.nz/seminar/ Upcoming Seminars to be held at the Department of Statistics, The University of Auckland en-nz http://www.stat.auckland.ac.nz/2012/seminar/#at-2012-02-16Thursday, 16 February 2012, 4:00 pm; Dr. Benoit Liquet, INSERM, Victor Segalen University, Bordeaux 2; Abstract: The talk discusses Akaike and likelihood crossvalidation criteria for model/estimator choice. After a presentation of the main concept on model selection, we will focus on the choice of estimators in non-standard cases. First, we study two examples arising when we wish to assess the quality of estimators on a particular set of information, while the estimators may use a larger set of information. The first example occurs when we construct a model for an event which happens if a continuous variable is above a certain threshold. We can compare estimators based on the observation of only the event or on the whole continuous variable. The other example is that of predicting survival based on survival information only, or using in addition information on patient's disease. We develop modified AIC and LCV criteria to compare estimators in this non-standard situation. Second, we study the choice of estimators in prognostic studies. Estimators for a clinical event may use repeated measurements of markers in addition to fixed covariates. These measurements can be linked to the clinical event by joint modelling involving latent structures. When the objective is to choose between different estimators based on joint models for prediction, the conventional Akaike information criterion (AIC) is not well adapted and decision should be based on predictive accuracy. We define an adapted risk function called expected prognostic cross entropy (EPCE) and further modify it for right-censored observations. The risk functions can be estimated by leave-one-out cross validation, for which we give approximate formulas and asymptotic distributions. James Curran2012-01-12 http://www.stat.auckland.ac.nz/2012/seminar/#at-2012-02-20Monday, 20 February 2012, 11:00 am; Professor Jim Hanley, Department of Epidemiology, Biostatistics, and Occupational Health, McGill University; Abstract: Influential reports on the reductions produced by screening for cancers of the prostate, colon and lung have appeared recently. The reported reductions in these randomized trials have been modest, and smaller than expected. But even more surprisingly, all three figures are very similar. I explain why these figures are underestimates and why the seemingly-universal 20% reduction is an artifact of the prevailing data-analysis methods and stopping rules. A different approach to the analysis of data from cancer screening trials is called for. James Curran2012-01-12 http://www.stat.auckland.ac.nz/2012/seminar/#at-2012-02-22Wednesday, 22 February 2012, 11:00 am; Professor Peter Jupp, U. St. Andrews; Abstract: Observations that are directions, axes, or rotations require the techniques of directional statistics. This talk aims to illustrate the special flavour of this area through glimpses at two topics. (a) Free-lunch learning Free-lunch learning (FLL) is a phenomenon in which relearning partially-forgotten mental associations induces recovery of other associations. When memory is modelled in terms of an artificial neural network, the extent of FLL can be quantified in geometrical terms and involves Grassmann manifolds of subspaces of the weight space. Joint work with Jim Stone (Psychology, Sheffield) will be described, in which simple properties of uniform distributions yield results on the expected amount of FLL. The form of forgetting plays an important role. (b) Crystals, earthquakes and orthogonal axial frames Orthogonal axial frames are (ordered) sets of orthogonal axes. They arise as (i) key geometrical elements (known in seismology as `focal mechanisms') of earthquakes, (ii) principal axes of certain physical tensors (e.g. stress tensors), (iii) axes of orthorhombic crystals. Some tools for the analysis of data that are orthogonal axial frames will be will be described. This is joint work with Richard Arnold (Wellington). Mark Holmes2012-01-14 http://www.stat.auckland.ac.nz/2012/seminar/#at-2012-03-08Thursday, 8 March 2012, 4:00 pm; Dr. Rolf Turner, Department of Statistics, University of Auckland; Abstract: It is a well-known phenomenon that airline passengers travelling on the same flight (same origin and same destination) and in the same class (cabin) will often have paid substantially different fares. This apparent anomaly in the pricing pattern is due to the fact there is a time-varying elasticity of demand (or "price sensitivity") for this particular "product". My co-author Pradeep Banerjee and I have developed a differential equations model which permits one to derive an optimal pricing policy in such a setting. (The policy is "optimal" in terms of the expected value of a stock of goods at a specified time.) Deriving the optimal policy requires a model for the price sensitivity and for an inhomogeneous Poisson arrival rate of customers. So far we have worked with smooth price sensitivity functions. However it is somewhat easier to translate intuitive conjectures about price sensitivity into a function framed as being piecewise linear in price. In this talk I will explain a bit about how the differential equations for the optimal prices are derived, and then discuss how the technique must be adjusted to deal with the piecewise linear setting. I will also discuss some of the techniques that I and my Summer Scholarship student Ray Shahlori have used to code up the solution procedure in R. I will show some examples of solutions. James Curran2012-01-13