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In recent years, we have seen a diverse range of crises and controversies concerning food safety, animal health and environmental risks including foot and mouth disease, dioxins in seafood, GM crops and more recently the safety of Irish pork. This has led to the recognition that the handling of uncertainty in risk assessments needs to be more rigorous and transparent. This would mean that decision makers and the public could be better informed on the limitations of scientific advice. The expression of the uncertainty may be qualitative or quantitative but it must be well documented. Various approaches to quantifying uncertainty exist, but none are yet generally accepted amongst mathematicians, statisticians, natural scientists and regulatory authorities. In this thesis we discuss the current risk assessment guidelines which describe the deterministic methods that are mainly used for risk assessments. However, probabilistic methods have many advantages, and we review some probabilistic methods that have been proposed for risk assessment. We then develop our own methods to overcome some problems with the current methods. We consider including various uncertainties and looking at robustness to the prior distribution for Bayesian methods. We compare nonparametric methods with parametric methods and we combine a nonparametric method with a Bayesian method to investigate the effect of using different assumptions for different random quantities in a model. These new methods provide alternatives for risk analysts to use in the future.