Project: Neural network-based left ventricle geometry prediction from CMR images with application in biomechanics
joint with Lukasz Romaszko, Alan Lazarus, David Dalton, Colin Berry, Xiaoyu Luo, Dirk Husmeier and Hao Gao
published in Artificial Intelligence in Medicine, 2021
Project: Gaussian Process Enhanced Semi-Automatic ABC: Parameter Inference in a Stochastic Differential Equation System for Chemotaxis
joint with Diana Giurghita and Dirk Husmeier
published in Journal of Computational Physics, 2020
Project: Partially Censored Posterior for Robust and Efficient Risk Evaluation
joint with Lennart Hoogerheide, Siem Jan Koopman and Herman K. van Dijk
published in Journal of Econometrics, 2020
Project: Time-varying Combinations of Bayesian Dynamic Models and Equity Momentum Strategies
joint with Nalan Baştürk, Stefano Grassi, Lennart Hoogerheide and Herman K. van Dijk
published in Journal of Econometrics, 2018
Project: Bayesian Dynamic Modeling of High-Frequency Integer Price Changes
joint with István Barra and Siem Jan Koopman
published in Journal of Financial Econometrics, 2018
Project: Closed-loop effects for modelling and inference in a pulmonary hypertension model
joint with Mihaela Paun, Mitchel J. Colebank, Mette S. Olufsen and Dirk Husmeier
Project: Predicting left ventricle geometries
joint with Lukasz Romaszko, Alan Lazarus, Hao Gao, Xiaoyu Luo and Dirk Husmeier
Submitted and under review
Methods for Accurate and Efficient Bayesian Analysis of Time Series, PhD Thesis
This thesis investigates Bayesian inference over time series models with the emphasis put on applications in economics and finance. We adopt simulation-based techniques which are necessary in any nontrival problem in this setting. The main motivation behind the presented research is to increase the effciency and accuracy of these computationally intensive methods in several different contexts. One of the main topics addressed is efficient and precise risk estimation, or rare event analysis. Another problem studied in this thesis is the efficiency of various sampling algorithms, in particular importance sampling (IS) and Markov chain Monte Carlo (MCMC) algorithms. Finally, we address the issue of forecasting, from a single model as well as from a combination of models.
Bayesian Risk Evaluation using Importance Sampling, MPhil Thesis in Econometrics
We consider the evaluation of two financial risk measures, Value at Risk and Expected Shortfall. Our analysis is performed in a Bayesian fashion where we adopt a model-based approach. We employ the Quick Evaluation of Risk using Mixture of t approximation algorithm (QERMit) of Hoogerheide and van Dijk (2010) due to its accuracy and efficiency, and we upgrade its basic framework in two ways. First, we replace the originally used posterior approximation algorithm with a superior, flexible technique. We report a substantial gain in the accuracy and the precision of estimates in our empirical application based on the daily S&P 500 returns. Second, we extend the basic QERMit framework to allow for latent variables in the underlying model. In this way, the developed technique can be applied to the class of the parameter driven models. We illustrate the procedure using a series of daily IBM returns. Noticeably, all the employed methods are based on importance sampling, which allows for fast computations and is not subject to convergence problem inherent to the alternative Markov Chain Monte Carlo methods.
Sequential Monte Carlo: Selected topics, Bachelor Thesis in Mathematics
We analyse the problem of inference about a latent signal governing the dynamics of a system given only the observed noisy data. We adopt the discrete-time state space approach due to the wide range of problems it can capture. Because in general no closed-form solution are available in this framework, we discuss the class of methods used for approximating of the posterior state distributions, called Sequential Monte Carlo. These methods are based on the Dirac-measures which stem from the draws (particles) from the distribution constructed in the previous iteration. A special attention is devoted to the filtering problem, where one is interested in the estimation of the current state of the system given the current system measurements. We derive theoretical forms of the particle filters, which we then use to construct algorithms suitable for numerical analysis. We discuss the degeneracy problem, inherent to the sequential importance sampling and selected methods to tackle it. The basic convergence results in the context of particle filters are presents. Finally, we consider three numerical application.
The Application of the DSGE-VAR Model to the Polish Macroeconomic Data, Master Thesis in Economics
The DSGE-VAR approach enables to combine the advantages of the theoretically consistent structural models with those of the empirical ones, characterised by the substantial degree of data fit. Moreover, the Bayesian estimation provides a convenient framework to incorporate initial beliefs about the model parameters into the estimation procedure, which seems to be particularly advantageous in the case of rather short time series for Poland. Finally, the obtained estimates allow to assess the extend of the DSGE model misspecification.