This paper demonstrates that there is a robust statistical relationship between the records of the global mean surface air temperature and the atmospheric concentration of carbon dioxide over the period 1870-1991. As such, the enhanced greenhouse effect is a plausible explanation for the observed global warming. Long term natural variability is another prime candidate for explaining the temperature rise of the last century. Analysis of natural variability from paleo-reconstructions, however, shows that human activity is so much more likely an explanation that the earlier conclusion is not refuted. But, even if one believes in large natural climatic variability, the odds are invariably in favour of the enhanced greenhouse effect. The above conclusions hold for a range of statistical models, including one that is capable of describing the stabilization of the global mean temperature from the 1940s to the 1970s onwards. This model is also shown to be otherwise statistically adequate. The estimated climate sensitivity is about 3.8°C with a standard deviation of 0.9°C, but depends slightly on which model is preferred and how much natural variability is allowed. These estimates neglect, however, the fact that carbon dioxide is but one of a number of greenhouse gases and that sulphate aerosols may well have dampened warming. Acknowledging the fact that carbon dioxide is used as a proxy for all human induced changes in radiative forcing brings a lot of additional uncertainty. Prior knowledge on both climate sensitivity and radiative forcing is needed to say anything about the respective sizes. A fully Bayesian approach is used to combine expert knowledge with information from the observations. Prior knowledge on the climate sensitivity plays a dominant role. The data largely exclude climate sensitivity to be small, but cannot exclude climate sensitivity to be large, because of the possibility of strong negative sulphate forcing. The posterior of climate sensitivity has a strong positive skewness. Moreover, its mode (again 3.8 °C; standard deviation 2.4°C) is higher than the best guess of the IPCC.