Predictive Causal Inference in A Series Of Events

Abstract

Consider a sequence of k events C₁, C₂…,C _k , and denote the vector of their occurrence times by S = (S₁,…, S _k ). Let each event be connected to other events in the sequence either directly or by intervening events as in Figure 2.1. Assume that the sequence of events is a causal chain and let C _k = E be the response or the “ultimate effect” (E) in the chain. Assume furthermore, that the chain is ordered; i.e., for the occurrence times holds S_r-1 < S_r whenever S_r-1 < ∞, r = 2, …, k. Then the chain is “forward going”. By the notation C → E we shall throughout mean “C causes E” in the probabilistic sense if not otherwise mentioned.