14:00 – 15:00 Karthik Bharath

Title: The shape space of functional data

Abstract: Qualitative descriptions of the shape of a function (e.g., convex, monotone, bimodal) and their use in developing and evaluating methodological tools abound in functional data analysis. The shape of a function is inextricably tied to its amplitude. A common approach to access shape information in a functional dataset is through a registration or alignment procedure to decouple amplitude from phase variations, which inevitably affects any downstream analysis. A hitherto unexplored alternative is to work directly with the shape space defined as the quotient of the function space under a group of shape-preserving transformations that treats phase as nuisance. I will discuss a stratified geometry for such a shape space that has regions of non-positive and (positive) unbounded curvature and discuss its statistical implications when analysing functional data.

15:30 – 16:30 Hector McKimm

Title: Sampling using Adaptive Regenerative Processes

Abstract: Enriching Brownian Motion with regenerations from a fixed regeneration distribution μ at a particular regeneration rate κ results in a Markov process that has a target distribution π as its invariant distribution. We introduce a method for adapting the regeneration distribution, by adding point masses to it. This allows the process to be simulated with as few regenerations as possible, which can drastically reduce computational cost. We explore the effectiveness of this self-reinforcing process at sampling from a number of target distributions. The examples show that our adaptive method allows regeneration-enriched Brownian Motion to be used to sample from target distributions for which simulation under a fixed regeneration distribution is computationally intractable.

Refreshments available between 15:00 – 15:30