Integrative Directed Cyclic Graphical Models with Heterogeneous Samples
In this talk, I will introduce novel hierarchical directed cyclic graphical models to infer gene networks by integrating genomic data across platforms and across diseases. The proposed model takes into account tumor heterogeneity. In the case of data that can be naturally divided into known groups, we propose to connect graphs by introducing a hierarchical prior across group-specific graphs, including a correlation on edge strengths across graphs. Thresholding priors are applied to induce sparsity of the estimated networks. In the case of unknown groups, we cluster subjects into subpopulations and jointly estimate cluster-specific gene networks, again using similar hierarchical priors across clusters. Two applications with multiplatform genomic data for multiple cancers will be presented to illustrate the utility of our model. I will also briefly discuss my other work and future directions.
Comonotonic risk measures in a world without risk-free assets
We focus on comonotonic risk measures from the point of view of the primitives of the theory as initially laid down by Artzner et al. (1999): acceptance sets and eligible assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligible asset. In fact, in many important cases, comonotonicity is only compatible with risk-free eligible assets. These findings seem to question the assumption of comonotonicity in a world of ``discounted'' capital positions and call for a renewed assessment of the meaning and the role of comonotonicity within a capital adequacy framework. Time permitting, we will also discuss some implications for insurance pricing.
Price Dynamics in a General Markovian Limit Order Book
We propose a simple stochastic model for the dynamics of a limit order book, extending the recent work of Cont and de Larrard, where the price dynamics are endogenous, resulting from market transactions. We also show that the diffusion limit of the price process is the so-called Brownian meander.
Statistical methods for pooled biomarker data
For many health outcomes, it has become increasingly common to aggregate data from multiple studies to obtain increased sample sizes. The enhanced sample size of the pooled data allows investigators to perform subgroup analyses, evaluate the dose-response relationship over a broad range of exposures, and provide robust estimates of the biomarker-disease association. However, study-specific calibration processes must be incorporated in the statistical analyses to address between-study variability in the biomarker measurements. We introduce methods for evaluating the biomarker-disease relationship that validly account for the calibration process. We consider both internal and external calibration studies in the context of nested and unmatched case-control studies. We then illustrate the utility of these estimators using simulations and an application to a circulating vitamin D and colorectal cancer pooling project.