Probabilistic Token Causation: A Bayesian Perspective

Abstract

Many authors (e.g., Good [8, 9] and Eells [5, 6]) distinguish between two kinds of probabilistic causality: the tendency of C to cause E and the degree to which C actually caused E. The former, a generic form of causation, can be discussed by comparing two prediction probabilities, one conditional on the occurrence of C and the other on its “counterfactual” event, where C does not occur. The latter, a singular form, is often called token causality and corresponds to finding a causal explanation of the occurrence of an event after it has been observed to happen. The purpose of this chapter is to formulate token causality by using the mathematical framework of marked point processes (MPPs) and their associated prediction processes. The same framework was used by Arjas and Eerola [2] for considering predictive causality. Therefore, this chapter can also be seen as an attempt to bridge the gap between these two types of causality reasoning.