Decision Trees

Statistical decision-making is widely used in experimental earth sciences. The topic plays an even more important role in Environmental Sciences due to the time varying nature of a system under observation and the possible necessity to take corrective actions. A set of possible corrective actions is usually available in a decision-making situation. Such a set is also known as the set of decisions. A number of observations of physical attributes (or variables) would also be potentially available. It is desirable for the corrective action selected in a situation to minimize the damage or cost, or maximize the benefit. Considering that a cost is a negative benefit, scientists and practitioners develop a composite single criterion that should be minimized, for a given decision-making problem. A best decision, one that minimizes the composite cost criterion, is also known as an optimal decision.

The process of obtaining or collecting the values that the physical variables take in an event is also known by other names such as extracting features (or feature variables) and making measurements of the variables. The variables are also called by other names such as features, feature variables, and measurements. Among the many possible physical variables that might influence the decision, collecting some of them may pose challenges. There may be a cost, risk, or some other penalty associated with the process of collecting some of these variables. In some other cases, the time delay in obtaining the measurements may also add to the cost of decision-making. This may take the form of certain losses because a corrective action could not be implemented earlier due to the time delay in the measurement process. These costs should be included in the overall cost criterion. Therefore, the process of decision-making may also involve deciding whether or not to collect some of the measurements.