Motivation

In environmental science and many other subjects there is certainly no shortage of uncertainty, for example, in our knowledge about whether it will rain or not tomorrow. Uncertainty about such events arises naturally from errors and gaps in measurements, incomplete and incorrect knowledge of the underlying mechanisms, and also from the overall complexity of all the possible interactions in real-world systems. We try to describe this uncertainty qualitatively by using words such as ``likely'', ``probably'', ``chance'', etc.. However, to make progress scientifically it is necessary to use a more quantitative definition of uncertainty. In 1812, the French mathematician Pierre Simon Laplace defined the word ``probability'' to mean a number lying between 0 and 1 that measures the amount of certainty for an event to occur. A probability of 1 means the event is completely certain to occur, whereas a probability of 0 means that the event will certainly never occur. Probability is essential for understanding how samples of data can be drawn from the underlying population, and for making inferences about this population based on sample statistics.