## 1 Introduction
### Literature Review
[PERSON] and [PERSON] (2018) applied additive quantile regression to model global horizontal irradiance. They used long-range dependence models on three sites based in South Africa and found that all the models were anti-persistent. Furthermore, in [PERSON] et al. [4], the authors looked at the clustering of solar irradiance patterns related to cloud cover forecasting from climate predictions using numerical data for the forecasting of solar power or irradiance for the following day. [PERSON] et al. [13] used a generalised ensemble model incorporating deep learning methods to come up with solar power predictions. A comparison of the performance of this method was done against support vector regression, deep belief network and random forest regression models and their results showed that their proposed method was the best. [PERSON] et al. [14] applied GPR for energy predictions using the Bayesian framework. In [PERSON] and [PERSON] [15], the authors worked on a study applying Gaussian process models to forecast solar power for 37 residential sites in a town called Adelaide in Australia. They used an integrated multi-site model without using prior data de-trending, this was achieved by capturing diurnal cycles, and discovered that the multi-site modelling was better than the single-site methods with varying weather conditions. In [PERSON] et al. [16], the authors did a forecasting study on GHI by applying GPR basing their study on kernel study. They applied several kernels and found that the quasi-periodic kernels outperformed most of them. Research on forecasting of solar power using grouped Gaussian processes was done by [PERSON] and [PERSON] [17]. They applied to multitask GP models with observations being linear with several latent node functions and also based on weight functions on priors. They used grouped coupled priors to solve spatial dependence between functions. Their method improved forecasting accuracy as compared to benchmark models used. [PERSON] [18] did research making use of a Bayesian framework to obtain sparse solutions to regression and classification of tasks applying linear parameter models. The research adopted a method called relevant vector machine (RVM) and a function family of the support vector machine (SVM). They found that the Bayesian method provides accurate values which make use of fewer basic functions than the SVM. [PERSON] [19] applied Gaussian processes and relevance vector machines from a Bayesian perspective not applying sampling methods of their interest in computational effection models. They worked on an improved RVM which showed that it had better predictive power. They also looked at another type of GP called reduced rank Gaussian processes (RRGPs) which are equivalent to the infinite extended linear models. Their results proved that the GPs will encounter a problem of the appropriateness of predictiveness of predictive variances, which was solved by modifying the classic RRGP. GPs and RVMs were used to derive equations for predicting uncertainty in time series that is multi-step allowing predictive uncertainties. [PERSON] and [PERSON] [20] studied probabilistic Bayesian analysis by applying a joint relationship between Gaussian processes and relevance vector machines. They used these to come up with a framework to view these approaches by applying kernel ridge regression and drawing connections among them by including aspects such as filtering, smoothing and interpolation. A relationship between these methods and the other methods such as linear kernel smoothers, Kalman filtering, smoothing and interpolation was studied. The results showed that the GP had a good behaviour of the predictive variance but it is restricted by the choice of a kernel function and its results of Kalman smoothing produced the same results.