Game-Theoretic Foundations for Probability and Finance

10Using Testing Protocols in Science and Technology

Probability has become ubiquitous in science and technology. Probabilities appear in scientific theories and in models used for control, prediction, and decision making. But usually only some aspects of a process are susceptible to probabilistic prediction. Using examples from science and mathematical statistics, this chapter shows how testing protocols can focus on the predictable aspects while respecting the unpredictability or unobservability of other aspects.

The role of information that is not forecast depends on whether we consider goals for Skeptic or goals for Forecaster. As we learned in Parts I and II, a typical result in game‐theoretic probability says that Skeptic can guarantee a disjunction: either Forecaster and Reality agree in some respect or the capital Skeptic risks is multiplied by a large factor. According to our mathematics, Skeptic can guarantee this disjunction regardless of what other events, predictable or not, transpire – regardless of anything else Skeptic or the other players already know or witness in the course of play. In contrast, what Forecaster can accomplish is an empirical or scientific question. Given all his information, including information that may unexpectedly become available in the course of play, can Forecaster keep Skeptic from multiplying the capital he risks by a large factor? If so, we say that Forecaster is reliable. If he manages to be consistently reliable by following a strategy ...