Title : Poincaré type inequalities on Hamming cube via martingale inequalities.
Abstract : Harmonic analysis is intimately related with martingale estimates.
But there is another type of discrete analysis, namely, harmonic analysis on Hamming cube (the math. foundation of Big Data science) that seemed to be disjoint from this relationship. We show how many classical (and some new) estimates on Hamming cube follow from martingale estimates. We also show why this is related to solving certain non-linear PDE of Monge–Ampère type and with classical inequalities in Gaussian spaces.
Speaker: Gideon Zamba (U. Iowa)
Title: Recurrence of Subsequent Malignancies following Diagnosis of and Treatment for Hodgkin Lymphoma Diagnosis
Abstract: Hodgkin’s Lymphoma (HL) is a type of cancer that affects the lymphatic system and compromises the body’s ability to fight infection. HL typically starts in white blood cells. HL occurs when a specific type of cell, the Reed-Stenberg cell, is present in the host’s system, causing the body’s infection fighting cells to develop a mutation in their DNA. Each year, there are several thousand people in the United States and worldwide who develop HL. Although there are many prognostic factors for HL and post treatment malignancies, it has also been hypothesized that initial treatment after diagnosis may be associated with subsequent new malignancies or death. We explored the association between prognostic factors and subsequent malignancies using the Oncology Registry at the University of Iowa Hospitals and Clinics. In this exploration we account for subject random effect through a gamma frailty model for recurrent events, which acts multiplicatively and jointly on both the hazard of new malignancies and the hazard of death. The parameters of the model were iteratively estimated using a penalized marginal likelihood approach. The findings suggest a significant within subject correlation, and a significant treatment effect on both the hazard of recurrence and the hazard of death.
Speaker: Elizabeth Gross (San Jose State U.)
Title: Goodness of fit of statistical network models
Abstract: Exponential random graph models (ERGMs) are families of distributions defined by a set of network statistics and, thus, give rise to interesting graph theoretic questions. Indeed, goodness-of-fit testing for these models can be achieved if we know how to sample uniformly from the space of all graphs with the same network statistics as the observed network. Examples of commonly used network statistics include edge count, degree sequences, k-star counts, and triangle counts. In this talk, we will introduce exponential random graph models, discuss the geometry of these models, and show the role toric ideals play in determining the quality of model fit.