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Statistical causality and measurable separability of σ-algebras

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  • Valjarević, Dragana
  • Merkle, Ana

Abstract

In this paper we consider a concept of statistical causality, based on Granger’s definition of causality and analyze the relationships between given causality and the concept of measurable separability of σ-algebras. The measurable separability of σ-algebras is defined in Florens et al. (1990). We give a generalization of that definition for flows of information represented by filtrations and consider some properties of measurable separability that are directly connected to the concept of statistical causality. Also, we apply some of these results on Bayesian experiment.

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  • Valjarević, Dragana & Merkle, Ana, 2021. "Statistical causality and measurable separability of σ-algebras," Statistics & Probability Letters, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:stapro:v:177:y:2021:i:c:s0167715221001280
    DOI: 10.1016/j.spl.2021.109166
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    References listed on IDEAS

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    1. Florens, J.P. & Mouchart, M., 1982. "A note on noncausality," LIDAM Reprints CORE 479, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    3. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    4. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-591, May.
    5. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    6. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    7. MOUCHART, Michel & ROLIN, Jean-Marie, 1985. "A note on conditional independence with statistical applications," LIDAM Reprints CORE 630, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Valjarević, Dragana & Petrović, Ljiljana, 2020. "Statistical causality and separable processes," Statistics & Probability Letters, Elsevier, vol. 167(C).
    9. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
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    Cited by:

    1. Merkle, Ana, 2023. "Causal predictability and weak solutions of the stochastic differential equations with driving semimartingales," Statistics & Probability Letters, Elsevier, vol. 197(C).

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