Thesis (M.Sc. (Statistics)) -- University of Limpopo, 2020 / Malaria is a mosquito borne disease, a major cause of human morbidity and mortality in most of the developing countries in Africa. South Africa is one of the countries with high risk of malaria transmission, with many cases reported in Mpumalanga and Limpopo provinces. Bayesian and classical methods of estimation have been applied and compared on the effect of climatic factors (rainfall, temperature, normalised difference vegetation index, and elevation) on malaria incidence. Credible and confidence intervals from a negative binomial model estimated via Bayesian estimation-Markov chain Monte Carlo process and maximum likelihood, respectively, were utilised in the comparison process. Bayesian methods appeared to be better than the classical method in analysing malaria incidence in the Limpopo province of South Africa. The classical framework identified rainfall and temperature during the night to be the significant predictors of malaria incidence in Mopani, Vhembe and Waterberg districts of Limpopo province. However, the Bayesian method identified rainfall, normalised difference vegetation index, elevation, temperature during the day and temperature during the night to be the significant predictors of malaria incidence in Mopani, Sekhukhune, Vhembe and Waterberg districts of Limpopo province. Both methods also affirmed that Vhembe district is more susceptible to malaria incidence, followed by Mopani district. We recommend that the Department of Health and Malaria Control Programme of South Africa allocate more resources for malaria control, prevention and elimination to Vhembe and Mopani districts of Limpopo province. Future research may involve studies on the methods to select the best prior distributions. / National Research Foundation (NRF)