Conducting Causal Analysis by Means of Approximating Probabilistic Truths

Bo Pieter Johannes Andrée*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


The current paper develops a probabilistic theory of causation using measure-theoretical concepts and suggests practical routines for conducting causal inference. The theory is applicable to both linear and high-dimensional nonlinear models. An example is provided using random forest regressions and daily data on yield spreads. The application tests how uncertainty in short-and long-term inflation expectations interacts with spreads in the daily Bitcoin price. The results are contrasted with those obtained by standard linear Granger causality tests. It is shown that the suggested measure-theoretic approaches do not only lead to better predictive models, but also to more plausible parsimonious descriptions of possible causal flows. The paper concludes that researchers interested in causal analysis should be more aspirational in terms of developing predictive capabilities, even if the interest is in inference and not in prediction per se. The theory developed in the paper provides practitioners guidance for developing causal models using new machine learning methods that have, so far, remained relatively underutilized in this context.

Original languageEnglish
Article number92
Pages (from-to)1-24
Number of pages24
Issue number1
Publication statusPublished - Jan 2022

Bibliographical note

Special Issue: Causal Inference for Heterogeneous Data and Information Theory.

Publisher Copyright:
© 2022 by the author. Licensee MDPI, Basel, Switzerland.


  • Approximation theory
  • Bitcoin
  • Causality
  • Correct specification
  • Hellinger distance
  • Inflation
  • Kullback–Leibler divergence
  • Misspecified models
  • Yield spreads


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