Consistency of stepwise uncertainty reduction strategies for Gaussian processes
Freitag, 27.4.18, 12:00-13:00, Raum 404, Ernst-Zermelo-Str. 1
In the first part of the talk, we will introduce spatial Gaussian processes.\nSpatial Gaussian processes are widely studied from a statistical point of view, and have found applications in many fields, including geostatistics, climate science and computer experiments. Exact inference can be conducted for Gaussian processes, thanks to the Gaussian conditioning theorem. Furthermore, covariance parameters can be estimated, for instance by Maximum Likelihood.\nIn the second part of the talk, we will introduce a class of iterative sampling strategies for Gaussian processes, called 'stepwise uncertainty reduction' (SUR). We will give examples of SUR strategies which are widely applied to computer experiments, for instance for optimization or detection of failure domains. We will provide a general consistency result for SUR strategies, together with applications to the most standard examples.
Volatility estimation for stochastic PDEs using high-frequency observations
Freitag, 8.6.18, 12:00-13:00, Raum 404, Ernst-Zermelo-Str. 1
Motivated by random phenomena in natural science as well as by mathematical finance, stochastic partial differential equations (SPDEs) have been intensively studied during the last fifty years with a main focus on theoretical analytic and probabilistic aspects. Thanks to the exploding number of available data and the fast progress in information technology, SPDE models become nowadays increasingly popular for practitioners, for instance, to model neuronal systems or interest rate fluctuations to give only two examples. Consequently, statistical methods are required to calibrate this class of complex models.\nWe study the parameter estimation for parabolic, linear, second order SPDEs observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide an explicit and easy to implement method of moments estimator based on the squared increments of the process. The estimator is consistent and admits a central limit theorem. This is established moreover for the estimation of the integrated volatility in a semi-parametric framework. Starting from a representation of the solution as an infinite factor model and exploiting mixing properties of Gaussian time series, the theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in a simulation study.\nThis is joint work with Markus Bibinger.
Learning Genetic Architecture of Complex Traits Across Populations
Freitag, 29.6.18, 12:00-13:00, Raum 404, Ernst-Zermelo-Str. 1
Genome-wide association studies (GWAS) have become a standard approach for identifying loci influencing complex traits. However, GWAS in non-European populations are hampered by limited sample sizes and are thus underpowered. We introduce an empirical Bayes approach, which improves the power of mapping trait loci relevant in minority populations through adaptively leveraging multi-ethnic evidence. Likewise, trans-ethnic information can improve genetic risk prediction of traits and diseases. I will discuss how these statistical approaches can be extended to integrate other types of biological knowledge.