A Language for Planning with Statistics

When a planner must decide whether it has enough evidence to make a decision based on probability, it faces the sample size prob­ lem. Current planners using probabilities need not deal with this problem because they do not generate their probabilities from ob­ servations. This paper presents an event­ based language in which the planner's proba­ bilities are calculated from the binomial ran­ dom variable generated by the observed ratio of one type of event to another. Such prob­ abilities are subject to error, so the planner must introspect about their validity. Infer­ ences about the probability of these events can be made using statistics. Inferences about the validity of the approximations can be made using interval estimation. Interval estimation allows the planner to avoid mak­ ing choices that are only weakly supported by the planner's evidence. 1 INTRODUCTION Planning relies on choosing the future actions most likely to be effective. Because actions are taken after they are planned, a planner's information is uncertain at planning time. Probabilities have been explored as a means of representing and reasoning about this uncertainty. In some domains, the necessary probabil­ ities can be gathered by querying experts in the field. If such experts do not exist, an agent must be able to infer probabilities from observations. This paper develops a language that combines Allen's temporal interval reasoning [ Allen, 1984) with statistical infer­ ence [ Bickel and Doksum, 1977) to facilitate planning using inferences about probabilities. If a planner must calculate its probabilities, it must decide when it has enough information to be confident of its calculations. Deciding when one is sufficiently confident of probabilities generated from observations is called the sample size problem. The sample size problem will be ubiquitous for planners that calculate probabilities from their experience. The most imme­ diate incarnation of this problem is that of deciding whether choices are warranted by the evidence. A planner should make its decisions based on the proba­ bilities about which it has good evidence, and discount the probabilities about which it is uncertain. One ap­ plication of making decisions based on strength of evi­ dence as well as probability is dealing with facts one is told. A planner may be told that a particular course of actions is better than another, but if its evidence is suf­ fi ciently strong, it may choose to ignore this informa­ tion. The sample size problem …