A Bayesian Approach to Yield Curve Modelling and Forecasting with Stochastic Volatility for Interest Rate Risk Management

This thesis explores how forecasts of Dutch government bond yields can be improved by extending the current Dynamic Nelson-Siegel (DNS) model, used by the Dutch State Treasury Agency (DSTA), with stochastic volatility modeling and a Bayesian approach to parameter estimation and forecasting. The primary goal was to determine if the model...

Monte Carlo algorithms for performing Bayesian inference on Piecewise Deterministic Processes

Since their introduction in 1993, particle filters are amongst the most popular algorithms for performing Bayesian inference on state space models that do not admit an analytical solution. In this thesis, we will present several particle filtering algorithms adapted to a class of models known as Piecewise Deterministic Markov Processes (PDMP), i...

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...

Efficient stochastic simulation on discrete spaces: Using balancing functions to incorporate local target density information into Markov Chain Monte Carlo sampling schemes

The breadth of theoretical results on efficient Markov Chain Monte Carlo (MCMC) sampling schemes on discrete spaces is slim when compared to the available theory for MCMC sampling schemes on continuous spaces. Nonetheless, in [Zan17] a simple framework to design Metropolis-Hastings (MH) proposal kernels that incorporate local information about...

Modelling Covid-19 in Delft using epidemiological models and Markov Chain Monte Carlo

The spread of Covid-19 is modelled in this Bachelor thesis. This is done using two compartmental epidemiological models: the SIR-model and SIRS-model. These models divide the population into three groups, namely Susceptible, Infected and Recovered. Artificial data is generated based on the stochastic version of the models. The models are applied...

Evaluating Stochastic Floating-Point Superoptimization with STOKE

The superoptimizer STOKE has previously been shown to be effective at optimizing programs containing floating-point numbers. The STOKE optimizer obtains these results by running a stochastic search over the set of all programs and selecting the best-optimized one. This study aims to find more clearly what floating-point programs STOKE optimizes...

The Metropolis-Hastings Method

In this report, our goal is to find a way to get some information such as the mean out of high dimensional densities. If we want to calculate the mean we need to calculate integrals, which are difficult to do for high dimensional densities. We cannot use the analytical or classical (deterministic) numerical rules for high dimensional problems...

How to determine the error of a Markov Chain Monte Carlo Output

This thesis discusses and compares methods which try to approximate the assymptotic variance.

Bayesian Identification of Thermodynamic Parameters from Shock Tube Data

The project concerns uncertainty reduction of parameters of a thermodynamic equation of state for a dense gas, using Bayesian inference. The dense gas considered is D6 siloxane and the equation of state used is the polytropic van der Waals equation. The shock tube data comes from the flexible asymmetric shock tube (FAST) experiment. This is...

Evaluation of inverse analysis methods with numerical simulation for slope excavation

Insufficient information on soil parameters and their spatial variability pose as a main factors of uncertainty in geotechnical design. When soil response differs from the expected, the notion of inverse analysis becomes relevant; back-calculating the parameter set able to reproduce the monitored observations. Accordingly, its application...