Next: Decision Trees Up: Decision Making Under Uncertainty: Previous: Introduction

# The Framework of Statistical Decision Theory

How do we reconcile uncertainties with the need for a decision now, recalling that a decision not to act until more information is available is still a decision? Risk analysis and statistical decision theory can provide some guidelines.

We've already encounted the most basic idea in decision theory in our discussion of the practical problems facing conservation biologists. Namely, the recognition from statistics that there are two types of errors we can make in evaluating an hypothesis:

• We may say that something is happening when it isn't (Type I), or

• We may say that something isn't happening when it is (Type II).

In classical statistics, an experimenter must decide beforehand the acceptable level of Type I error and design an experiment with an acceptable level of Type II error. The decision on whether to accept or reject the null hypothesis then depends only on the level of Type I error the experimenter is willing to accept, e.g., the conventional level of 5%.

An alternative approach, known as Bayesian statistics, treats the probability quite differently.1 Prior beliefs are combined with the likelihood of the data to produce posterior probabilities about the hypothesis. More importantly, Bayesians treat the decision of whether to accept or reject the null hypothesis as a real decision, i.e., as an action that has consequences. Moreover, they recognize that the cost of being wrong depends on how you're wrong. It is probably worse, for example, to decide that there is no evidence of a worldwide decline in amphibian populations when they are declining than to decide that there there is evidence for a worldwide decline when they are not declining. We have to remember that in conservation planning, you don't have the option of not deciding. At most you have the option of deciding not to decide, which is still a decision. Saying

``I don't know whether species X poses a significant threat to conservation values in area Y. Let me study the problem for five years and get back to you.''
is equivalent to saying
``I don't know whether species X poses a significant threat to conservation values in area y. But I know that any threat it poses is mild enough that I can afford to investigate the problem for five years before doing anything to reverse the threat.

Next: Decision Trees Up: Decision Making Under Uncertainty: Previous: Introduction
Kent Holsinger 2011-11-13