Abstract
Information theoretic (IT) approaches to quantifying causal influences have experienced some popularity in the literature, in both theoretical and applied (e.g., neuroscience and climate science) domains. While these causal measures are desirable in that they are model agnostic and can capture non-linear interactions, they are fundamentally different from common statistical notions of causal influence in that they (1) compare distributions over the effect rather than values of the effect and (2) are defined with respect to random variables representing a cause rather than specific values of a cause. We here present IT measures of direct, indirect, and total causal effects. The proposed measures are unlike existing IT techniques in that they enable measuring causal effects that are defined with respect to specific values of a cause while still offering the flexibility and general applicability of IT techniques. We provide an identifiability result and demonstrate application of the proposed measures in estimating the causal effect of the El Niño–Southern Oscillation on temperature anomalies in the North American Pacific Northwest.
Highlights
Consider a directed acyclic graph (DAG), where nodes represent random variables and edges represent a direct causal influence between two variables
We estimate the normalized STE, SNDE, and SNIE of El Niño–Southern Oscillation (ENSO) on temperature and the normalized conditional STE of the past temperature average on the average conditioned on ENSO
Displays two boxplots for each measure—the first shows the distribution of the measure estimated on the bootstrap samples and the second shows the distribution of the measure estimated under the null hypothesis that the causal link in question does not exist
Summary
Consider a directed acyclic graph (DAG), where nodes represent random variables and edges represent a direct causal influence between two variables. While IT measures yield the less interpretable unit of bits, they are able to capture more complex causal effects, for instance the effect that a variable has on the variance of another Acknowledging this difference helps to understand the disparity between the applications of statistical and IT measures. Using a conditional version of the proposed measures, we show the presence of a “persistence signal” across two-week average temperature anomalies that is modulated by the El Niño phase This result both demonstrates the value of the proposed framework and provides direction for future studies focused on climate scientific findings.
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