Temperature measurements are subject to uncertainties. Temperature observations are sparsely available over the surface of the earth. The uncertainties in temperatures due to these gaps in spatial coverage is quanti fied using multi-resolution lattice kriging (MRLK). These uncertainties are combined with the existing estimates of the observational uncertainties. It results in a monthly temperature data product from 1850-2016. A new approximate Bayesian methodology is proposed for spatial data analysis. It relies on spatial dependence of the data using the variogram. This methodology is integrated with the multi-resolution lattice kriging (MRLK) model. It results in an approximate Bayesian inference for MRLK. The MRLK with the approximate Bayesian framework is used to generate another temperature data set. It samples the observational and coverage uncertainties in temperatures but also accounts for the model parametric uncertainties. The two sets of monthly temperature data products created in this thesis provide the uncertainties in temperatures at a regional scale. Therefore, a probabilistic El Niño Southern Oscillation (ENSO) index is invented that reflects the regional estimates of temperature uncertainties. This defi nition is applied to both versions of temperature data sets. During the pre-industrial period, fewer temperature measurements are available. Therefore, there is uncertainty in the pre-industrial baseline temperatures. Uncertainties in the pre-industrial baseline are integrated with the observational, coverage and parametric uncertainties. The results suggest that the uncertainties mainly dominate early temperature records. However, the uncertainty in temperatures due to the uncertain pre-industrial baseline stays same throughout the time series.

This thesis uses state-of-the-art equilibrium models to analyse the impact of cap-and-trade (C&T) systems on regional electricity markets, which span areas subject to disparate carbon-reduction policies, e.g., only one area of the market is covered by a C&T. Such markets are vulnerable to carbon leakage, i.e., emission increase in the uncapped subregion as a result of imposing a C&T in the regulated subregion. Specifically, the focus is on the South-East Europe Regional Electricity Market (SEE-REM) for which an ex ante analysis of potential leakage into the non-EU ETS part is carried out considering the interaction of (i) an emission cap and hydropower availability and (ii) an emission cap and market power. In a perfectly competitive setting, a mixed-complementarity problem calibrated to SEE-REM is implemented for various C&T emission caps in order to estimate the extent of carbon leakage. The impact of market power is next incorporated using a bi-level model that is reformulated as a mathematical program with equilibrium constraints and implemented as a mixed-integer quadratic problem for SEE-REM in order to investigate how a dominant firm’s incentives to manipulate both electricity and carbon prices affect carbon leakage. Furthermore, in a theoretical framework, a bi-level model is developed where at the upper level, the policymaker determines an optimal emission cap over a subregion of an electricity market interconnected to the uncapped subregion. The purpose of this model is to establish the basis for a second-best anti-leakage measure.

Chemometrics has been applied to analyse near-infrared (NIR) spectra for decades. Linear regression methods such as partial least squares (PLS) regression and principal component regression (PCR) are simple and widely used solutions for spectroscopic calibration. My dissertation connects spectroscopic calibration with nonlinear machine learning techniques. It explores the feasibility of applying nonlinear methods for NIR calibration. Investigated nonlinear regression methods include least squares support vec- tor machine (LS-SVM), Gaussian process regression (GPR), Bayesian hierarchical mixture of linear regressions (HMLR) and convolutional neural networks (CNN). Our study focuses on the discussion of various design choices, interpretation of nonlinear models and providing novel recommendations and insights for the con- struction nonlinear regression models for NIR data. Performances of investigated nonlinear methods were benchmarked against traditional methods on multiple real-world NIR datasets. The datasets have differ- ent sizes (varying from 400 samples to 7000 samples) and are from various sources. Hypothesis tests on separate, independent test sets indicated that nonlinear methods give significant improvements in most practical NIR calibrations.

Multi-state models can be used to analyse processes where change of status over time is of interest. In medical research, processes are commonly defined by a set of living states and a dead state. Transition times between living states are often interval censored. In this case, models are usually formulated in a Markov processes framework. The likelihood function is then constructed using transition probabilities. Models are specified using proportional hazards for the effect of covariates on transition intensities. Time-dependency is usually defined by parametric models, which can represent a strong model assumption. Semiparametric hazards specification with splines is a more flexible method for modelling time-dependency in multi-state models. Penalised maximum likelihood is used to estimate these models. Selecting the optimal amount of smoothing is challenging as the problem involves multiple penalties. This thesis aims to develop methods to estimate multi-state models with splines for interval-censored data. We propose a penalised likelihood method to estimate multi-state models that allow for parametric and semiparametric hazards specifications. The estimation is based on a scoring algorithm, and a grid search method to estimate the smoothing parameters. This method is shown using an application to ageing research. Furthermore, we extend the proposed method by developing a computationally more efficient method to estimate multi-state models with splines. For this extension, the estimation is based on a scoring algorithm, and an automatic smoothing parameters selection. The extended method is illustrated with two data analyses and a simulation study.

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