Broadly, my research interests centre around building and evaluating models for statistical decision making and control of autonomous systems. These days, I mostly work on uncertainty modelling and statistical model evaluation in machine learning, especially Deep Learning, with a focus safety-critical applications such as autonomous driving.
More broadly, I am devoted to developing a rigorous statistical language and tools to ensure the safety and reliability of real-life machine learning applications. The largest part of my research so far has dealt with learning and decision strategies under uncertainty in probabilistic temporal models. In more detail, I have engaged in the study of
- sequential testing/estimation and quickest change-point detection problems in Bayesian Statistics,
- trading strategies and valuation of financial derivatives in Financial Mathematics,
- stochastic differential equations and stochastic filtering techniques.
Research papers
Article's subject area is provided in square brackets. Authors are listed in alphabetical order (convention in mathematical disciplines) unless stated otherwise.
Self-driving car safety quantification via component-level analysis [Autonomous Driving Safety, Statistics, Probabilistic Modelling]
Written in collaboration with T. Wiklund, A. Grigaite, A. Kalkauskas, I. Vysniauskas, S. Keen.
To appear in SAE International Journal of Connected and Automated Vehicles, 2021 (preprint on arxiv).
Evaluation of model calibration in classification [Machine Learning, Statistics, Probabilistic Modelling]
First author, written in collaboration with D. Widmann, C. Andersson, F. Lindsten, J. Roll, T. Schön.
Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), 2019 (preprint on arxiv, local pdf).
Bayesian sequential least-squares estimation for the drift of a Wiener process [Statistics, Probabilistic Modelling]
Written in collaboration with E. Ekström, I. Karatzas.
To appear in Stochastic Processes and Their Applications, 2019 (final version, preprint on arxiv, local pdf).
Optimal stopping of a Brownian bridge with an unknown pinning point [Probabilistic Modelling, Statistics]
Written in collaboration with E. Ekström.
Stochastic Processes and Their Applications, 2019 (final version, preprint on arxiv, local pdf).
Monotonicity and robustness in Wiener disorder detection [Probabilistic Modelling, Statistics]
Written in collaboration with E. Ekström.
Sequential Analysis, 2019 (final version, preprint on arxiv, local pdf).
Asset liquidation under drift uncertainty and regime-switching volatility [Financial Mathematics, Probabilistic Modelling]
Single author.
Applied Mathematics & Optimization, 2018 (final version, preprint on arxiv, local pdf).
Optimal liquidation of an asset under drift uncertainty [Financial Mathematics, Probabilistic Modelling]
Written in collaboration with E. Ekström.
SIAM Journal on Financial Mathematics, vol. 7, no. 1, 2016, pp. 357-381 (final version, preprint on arxiv, local pdf).
Bayesian sequential testing of the drift of a Brownian motion [Statistics, Probabilistic Modelling]
Written in collaboration with E. Ekström.
ESAIM: Probability and Statistics, vol. 19, 2015, pp. 626-648 (final version, preprint on arxiv, local pdf).
The 3/2-model as a stochastic volatility approximation for a large-basket price-weighted index [Financial Mathematics, Probabilistic Modelling]
Written in collaboration with B. Hambly.
International Journal of Theoretical and Applied Finance, vol. 18, 2015, ID 1550041 (final version, preprint as local pdf).
Theses
Optimal Sequential Decisions in Hidden-State Models
PhD thesis (Introduction with a summary of the included papers).
Defended on June 9, 2017, at Ångström Laboratory, Uppsala University..
Opponent: Prof. Huyên Pham, University Paris Diderot (Paris 7).
In the thesis, I found and investigated optimal statistical decision procedures for problems from Finance, Engineering, and Statistics.
Optimal Stopping under Drift Uncertainty
Licentiate thesis (Half-PhD thesis), Uppsala University, 2015 (final version, local pdf).
Reviewer: Dr Pavel Gapeev (London School of Economics).
Approximation of a large-basket index with an application to the pricing of variance options
Master's thesis, Oxford University, 2012.
Supervisor: Prof. Ben Hambly.