Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Estimation of computer waste quantities using forecasting techniques

Technology changes rapidly over years providing continuously more options for computer alternatives and making life easier for economic, intra-relation or any other transactions. However, the introduction of new technology “pushes” old Information and Communication Technology (ICT) products to non-use. E-waste is defined as the quantities of ICT products which are not in use and is bivariate function of the sold quantities, and the probability that specific computers quantity will be regarded as obsolete. In this paper, an e-waste generation model is presented, which is applied to the following regions: Western and Eastern Europe, Asia/Pacific, Japan/Australia/New Zealand, North and South America. Furthermore, cumulative computer sales were retrieved for selected countries of the regions so as to compute obsolete computer quantities. In order to provide robust results for the forecasted quantities, a selection of forecasting models, namely (i) Bass, (ii) Gompertz, (iii) Logistic, (iv) Trend model, (v) Level model, (vi) AutoRegressive Moving Average (ARMA), and (vii) Exponential Smoothing were applied, depicting for each country that model which would provide better results in terms of minimum error indices (Mean Absolute Error and Mean Square Error) for the in-sample estimation. As new technology does not diffuse in all the regions of the world with the same speed due to different socio-economic factors, the lifespan distribution, which provides the probability of a certain quantity of computers to be considered as obsolete, is not adequately modeled in the literature. The time horizon for the forecasted quantities is 2014-2030, while the results show a very sharp increase in the USA and United Kingdom, due to the fact of decreasing computer lifespan and increasing sales.