# Dr Dale Roberts

## Research interests

My research interests are in probability theory, stochastic processes, and their applications. I also actively engage and collaborate with Australian industry and government on real-world problems.

I teach the research-led course 'Big Data Statistics' (STAT3017) that looks at the application of random matrix theory in high-dimensional statistics and machine learning. Particular focus is on understanding how classic approaches break down when the dimensionality of the data becomes large and how these problems may be resolved using recent mathematical results.

I love programming, building my own research tools, and routinely release them on GitHub for others to use (see my profile). Many of my public projects are highly starred by the international community, my ranking is here.

## Biography

I graduated from the University of Technology, Sydney (UTS) with a first class Honours in Mathematics in 2006. After my honours I spent some time working in the finance industry. In 2012, I completed my Ph.D. in Mathematics at the University of New South Wales on the topic of Stochastic Partial Differential Equations (SPDE). On completing my PhD, I joined ANU as a Lecturer jointly appointed in RSFAS and the Mathematical Sciences Institute (MSI). At the start of 2014, I left the MSI and moved full-time to CBE/RSFAS. I was promoted to Senior Lecturer in 2014.

## Researcher's projects

For students seeking Honours or PhD supervision, some keywords to describe my mathematical interests are: stochastic differential equations, stochastic partial differential equations, partial differential equations, Lévy processes, Brownian motion, stochastic processes, random fields, random matrices, high-dimensional probability, random graphs, network theory, dynamics on graphs, high-dimensional statistics, multivariate statistics, statistical learning, machine learning, numerical analysis, numerical methods.

I also like taking these mathematical concepts and using them to solve real-world problems. As such, I also know a little about remote sensing (satellite imagery) and mathematical finance.

## Current student projects

- Emma Ai (PhD in Statistics)
- Timothy McLennan-Smith (PhD in Statistics)
- Rui Cheng (Honours in Statistics)
- Michael Winjen (Honours in Statistics)
- Omar Al-Ghattas (Research Associate)

## Past student projects

- Remy Hamilton-Smith. Statistical Learning applied to Burnscar Classification and Natural Hazard Insurance.
*First class**Honours in Actuarial Studies.* - Omar Al-Ghattas. Stochastic Portfolio Theory and Information-theoretical Portfolio Tracking.
*First class**Honours in Statistics.* - Chaturi Bhaskaran. Overshoots of random walks and Lévy processes.
*First class Honours in Mathematics.* - Nam Ho. Batch and sequential learning with complexity measures.
*First class Honours in Mathematics.* - Emma Ai. Multiwindowed barrier options under stochastic volatility.
*M.Phil. in Mathematics.* - Yang Liu. Existence and uniqueness of solutions to ODEs and SDEs with irregular coefficients.
*First class Honours in Mathematics.* - Anjisht Gosain. Pricing of Himalaya options under the Heston stochastic volatility model.
*First class Honours in Finance.* - Lindon Roberts. Wavelet methods for variational inequalities.
*First class Honours in Mathematics & University medal*.