Sticky PDMP samplers for sparse and local inference problems

We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing...

Analyzing point spread functions for multiple emitter fitting by posterior density estimation

The microscope is an essential tool for biologists. Since the late 16th century, it has given researchers a better understanding of cell processes and greatly advanced healthcare. In this century, Single molecule localization microscopy (SMLM) has revolutionized optical microscopy by breaking the optical diffraction limit. Sparsely activating...

Bayesian inference for discretely observed diffusion processes

In dit proefschrift bestuderen we diffusie processen, it zijn Markovprocessen met continue paden in een euclidische ruimte die bepaalde stochastische differentiaalvergelijkingen oplossen. Wij ontwikkelen en implementeren Bayesiaanse procedures voor de schatting van de drift en diffusie coefficienten wanneer slechts discrete observaties van het...

Contributions to the financial mathematics of energy markets

This thesis provides several contributions to quantitative finance for energy markets: electricity price modelling, implying oil price volatilities, pricing and hedging of exotic commodity options. Electricity spot prices are characterized by spikes (jumps) because electricity is non-storable. A widely used model for stochastic component of...