In this thesis we focus on pairwise comparison models. These models are well established in the field of statistics and are highly applicable in many areas, in particular in sports which motivated our work. We present several generalizations of the famous Bradley-Terry model for pairwise comparisons. The main extension we propose is to model the underlying time-varying latent strengths as Gaussian processes. Alternatively, we also apply barycentric rational interpolation and compare the two approaches. The outcome of pairwise comparisons are often not dependent solely on latent strengths but also on various external variables. For this reason we also extend our models to allow additional covariates. In sports there are often bookmaker odds data available. Bookmaker odds are known to be a source of accurate outcome probabilities, because bookmakers and the public are incentivized to use all available information. Our models allow for the inclusion of the information in the form of outcome probabilities. The empirical part of our research consists of comparing several models and inference methods on various sports data sets. We demonstrated that using Gaussian processes is advantageous compared to barycentric rational interpolation as they are more flexible in modelling sudden changes in the underlying latent strengths. When using barycentric rational interpolation, Bayesian inference gives better results than maximum likelihood estimation. In the case of Gaussian processes, Bayesian inference will give similar results as using Laplace approximation if hyper-parameters of the latter are determined by cross-validation rather than by marginal likelihood. With examples from sports we confirmed that using information from outcome probabilities from bookmaker odds further improves models' predictions and gives the best results. Using this additional information also results in less uncertainty in parameter estimates. We also implemented several Markov chain Monte Carlo algorithms specifically adapted for inference for Gaussian processes. We compared the Metropolis-Hastings algorithm and variants of the Gibbs algorithm with the Hamiltonian Monte Carlo algorithm. The latter algorithm as implemented in Stan gives superior results with respect to effective sample size and time efficiency.

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