Excursion Probabilities and Geometric Properties of Multivariate Gaussian Random Fields
Excursion probabilities of Gaussian random fields have many applications in statistics (e.g., scanning statistic and control of false discovery rate (FDR)) and in other areas. The study of excursion probabilities has had a long history and is closely related to geometry of Gaussian random fields. In recent years, important developments have been made in both probability and statistics.
In this talk, we consider the excursion probabilities of bivariate Gaussian random fields with non-smooth (or fractal) sample functions and study their geometric properties and excursion probabilities. Important classes of multivariate Gaussian random fields are those stationary with Matérn cross-covariance functions [Gneiting, Kleiber, and Schlather (2010)] and operator fractional Brownian motions which are operator-self-similar with stationary increments.
Background risk model and inference based on ranks of residuals
It is often easier to model the behaviour of a random vector by choosing the marginal distributions and the copula separately rather than using a classical multivariate distribution. Many copula families, including the classes of Archimedean and elliptical copulas, may be written as the survival copula of a random vector R(X,Y), where R is a strictly positive random variable independent of the random vector (X,Y). A unified framework is presented for studying the dependence structure underlying this stochastic representation, which is called the background risk model. However, in many applications, part of the dependence may be explained by observable external factors, which justifies the use of generalized linear models for the marginal distributions. In this case and under some conditions that will be discussed, the inference on the copula can be based on the ranks of suitable residuals.
Causal Inference for Complex Observational Data
Observational data often have issues which present challenges for the data analyst. The treatment status or exposure of interest is often not assigned randomly. Data are sometimes missing not at random (MNAR) which can lead to sample selection bias. And many statistical models for these data must account for unobserved confounding. This talk will demonstrate how to use standard maximum likelihood estimation to fit extended regression models (ERMs) that deal with all of these common issues alone or simultaneously.
To be announced (TBA)
To be announced (TBA)
The first Waterloo Conference in Statistics, Actuarial Science, and Finance (WATSAF1).
To be announced (TBA)
To be announced (TBA)
In 2019, the Master of Actuarial Science (MActSc) professional degree program will be celebrating 10 wonderful years at the University of Waterloo.
