Probabilistic forecasting plays a pivotal role both in the application and in the advancement of geophysical modelling. Operational techniques and modelling methodologies are examined critically in this thesis and suggestions for improvement are made; potential improvements are illustrated in low-dimensional chaotic systems of nonlinear equations. Atlantic basin hurricane forecasting and forecast evaluation methodologies on daily to multi-annual timescales provide the primary focus of application and real world illustration. Atlantic basin hurricanes have attracted much attention from the scientific and private sector communities as well as from the general public due to their potential for devastation to life and property, and speculation on increasing trends in hurricane activity. Current approaches to modelling, prediction and forecast evaluation employed in operational hurricane forecasting are critiqued, followed by recommendations for best-practice techniques. The applicability of these insights extends far beyond the forecasting of hurricanes. Hurricane data analysis and forecast output is based on small-number count data sourced from a small-sample historical archive; analysis benefits from specialised statistical methods which are adapted to this particular problem. The challenges and opportunities arising in hurricane statistical analysis and forecasting posed by small-number, small-sample, and, in particular, by serially dependent data are clarified. This will allow analysts and forecasters alike access to more appropriate statistical methodologies. Novel statistical forecasting techniques are introduced for seasonal hurricane prediction. In addition, a range of linear and non-linear techniques for analysis of hurricane count data are applied for the first time along with an innovative algorithmic approach for the statistical inference of regression model coefficients. A real-time outlook for the 2013 hurricane season is presented, along with a methodology to support a running (re)analysis for National Hurricane Center 48 hour forecasts in 2013; the focus here is on if, and if so how, to improve forecast effectiveness by “recalibrating” the raw forecasts in real time. In this case, it is revealed that recalibration does not improve forecast performance, and that, across years, it can be detrimental. In short, a new statistical framework is proposed for evaluating and interpreting forecast reliability, forecast skill, and forecast value to provide a sound basis for constructing and utilising operational event predictions. This novel framework is then illustrated in the specific context of hurricane prediction. Proposed methods of forecast recalibration in the context of both a low-dimensional dynamical system and operational hurricane forecasting are employed to illustrate methods for improving resource allocation distinguishing, for example, scenarios where forecast recalibration is effective from those where resources would be better dedicated towards improving forecast techniques. A novel approach to robust statistical identification of the weakest links in the complex chain leading to probabilistic prediction of nonlinear systems is presented, and its application demonstrated in both numerical studies and operational systems.