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The title of the thesis: Statistical methods for sequential decision making and inference

Thesis defender: Sahel Iqbal
Opponent: Prof. Jimmy Olsson, KTH Royal Institute of Technology, Sweden
Custos: Prof. Simo Särkkä, Aalto University School of Electrical Engineering

Sequential decision making under uncertainty appears in many areas of science and engineering: robots must act using noisy sensors, autonomous systems must learn from the consequences of their actions, and scientists must choose experiments that reveal as much information as possible from limited data. In all these cases, each decision affects not only the immediate outcome, but also what can be learned for future decisions.

This thesis develops statistical methods for such problems by treating decision making as a form of probabilistic inference. Instead of only asking which action is best right now, the methods reason about possible future actions and observations, and about how new information can improve later decisions. This provides a unified way to study optimal control, partially observed decision making, and sequential Bayesian experimental design.

The thesis introduces new algorithms based on sequential Monte Carlo methods, also known as particle methods. These algorithms use many simulated possibilities to represent uncertainty about hidden states, unknown parameters, observations, and decisions. The main result is a common inference-based framework that can handle nonlinear and non-Gaussian problems where many classical methods require restrictive approximations.

The included publications develop particle-based methods for designing informative sequences of experiments, optimizing policies in partially observed systems, and making these methods more efficient for long decision sequences. The thesis also applies the same probabilistic viewpoint to scientific computing by developing a parallel-in-time Bayesian method for solving time-dependent nonlinear partial differential equations.

The results can be applied in robotics, autonomous systems, sensor management, adaptive experimentation, and simulation-based engineering. More broadly, the thesis shows that decision making, experimental design, and numerical computation can be understood through the same probabilistic lens, leading to methods that better account for uncertainty and the value of information.

Key words: Sequential decision making, Bayesian inference, Sequential Monte Carlo, Experimental design, Partially observable systems, Probabilistic numerics, Uncertainty quantification.

Thesis available for public display 7 days prior to the defence at .

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