(CRM-, Joint-) Colloquium
Fridays 3:30pm, Room B005,
Coffee: Common Room, before the colloquium at 3pm.
(Carleton-uOttawa shuttle information)
In this talk I will give an informal introduction to the theory of quadratic forms, then discuss a theorem, proved jointly with Patrick Brosnan and Angelo Vistoli, which shows that there exist quadratic forms with surprisingly large Pfister numbers.
Methods This analysis combines very detailed statistical analysis of Statistics Canada’s longitudinal National Population Health Survey (NPHS), with the HealthPaths dynamic microsimulation model. Microsimulation is used to synthesize a realistic base-case representative longitudinal population sample, and then a series of carefully constructed counterfactual populations, each cutting a link in the “web of causality” estimated from the NPHS. Comparisons of the distributions of health-adjusted life lengths and summary HALE measures between counterfactuals and the base case are then used to estimate the quantitative importance of the determinants being analysed. Replicate simulations plus underlying replicate regressions further enable sophisticated measures of uncertainty in model results.
Findings This analysis extends an earlier version which focused on four factors -- obesity, smoking, education, and Antonovsky’s Sense of Coherence (SoC). In that analysis, surprisingly, SoC had the largest potential impact, while education and smoking each accounted for about half as many years of (cause-deleted) HALE, and obesity accounted for relatively little. This analysis extends these results to encompass a broader range of factors, including household income, leisure and daily physical activity, employment, sense of mastery, family membership, and institutional residence. These additions change the rank order and magnitudes of the factors somewhat, reflecting omitted variable biases. The statistical analysis has had to confront a number of challenges with the main data set, including “inertia” in health states, missing data, and errors in variables.
Interpretation Widely observed socioeconomic gradients in health, when examined in greater detail, are the culmination of myriad co-evolving dynamic processes, where their interacting and joint effects, alone, are each small. It is essential to employ an analytical framework that combines robust estimates of individual multivariate health status dynamics with health determinants dynamics in order to assess realistically the sources of health inequalities.
Biographical information: Professor Haagerup is among the world's leading mathematicians, having made ground-breaking contributions in a variety of areas ranging from operator algebras and operator theory to free probability, random matrices and applications in mathematical physics. Modern functional and harmonic analysis even reflects his tremendous influence through fundamental concepts bearing his name that have entered the mathematical lexicon, such as the Haagerup tensor product and the Haagerup property. His many honours include an invited lecture at the ICM 1986 (Berkeley) as well as plenary lectures at both the ICM 2002 (Beijing) and the ICMP 2012 (Aalborg). He received the 14th European Latsis Prize from the European Science Foundation in 2012, and presently holds an Advanced Grant from the European Research Council. He is a member of the Royal Danish Academy of Sciences and Letters, as well as the Norwegean Academy of Science and Letters.