### Abstract

In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable Y when the causal variable X is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In other words, the steps of the estimation of the intervention effect using the causal diagram are as follows: 1. Estimate the causal diagram from the data, 2. Estimate the probability distributions in the causal diagram from the data, 3. Calculate the intervention effect. However, if the problem of estimating the intervention effect is formulated in the statistical decision theory framework, estimation with this procedure is not necessarily optimal. In this study, we formulate the problem of estimating the intervention effect for the two cases, the case where the causal diagram is known and the case where it is unknown, in the framework of statistical decision theory and derive the optimal decision method under the Bayesian criterion. We show the effectiveness of the proposed method through numerical simulations.

Original language | English |
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Title of host publication | 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781728111513 |

DOIs | |

Publication status | Published - 2019 Apr 16 |

Event | 53rd Annual Conference on Information Sciences and Systems, CISS 2019 - Baltimore, United States Duration: 2019 Mar 20 → 2019 Mar 22 |

### Publication series

Name | 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019 |
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### Conference

Conference | 53rd Annual Conference on Information Sciences and Systems, CISS 2019 |
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Country | United States |

City | Baltimore |

Period | 19/3/20 → 19/3/22 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019*[8692816] (2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CISS.2019.8692816

**A Note on the Estimation Method of Intervention Effects based on Statistical Decision Theory.** / Horii, Shunsuke; Suko, Tota.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019.*, 8692816, 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019, Institute of Electrical and Electronics Engineers Inc., 53rd Annual Conference on Information Sciences and Systems, CISS 2019, Baltimore, United States, 19/3/20. https://doi.org/10.1109/CISS.2019.8692816

}

TY - GEN

T1 - A Note on the Estimation Method of Intervention Effects based on Statistical Decision Theory

AU - Horii, Shunsuke

AU - Suko, Tota

PY - 2019/4/16

Y1 - 2019/4/16

N2 - In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable Y when the causal variable X is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In other words, the steps of the estimation of the intervention effect using the causal diagram are as follows: 1. Estimate the causal diagram from the data, 2. Estimate the probability distributions in the causal diagram from the data, 3. Calculate the intervention effect. However, if the problem of estimating the intervention effect is formulated in the statistical decision theory framework, estimation with this procedure is not necessarily optimal. In this study, we formulate the problem of estimating the intervention effect for the two cases, the case where the causal diagram is known and the case where it is unknown, in the framework of statistical decision theory and derive the optimal decision method under the Bayesian criterion. We show the effectiveness of the proposed method through numerical simulations.

AB - In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable Y when the causal variable X is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In other words, the steps of the estimation of the intervention effect using the causal diagram are as follows: 1. Estimate the causal diagram from the data, 2. Estimate the probability distributions in the causal diagram from the data, 3. Calculate the intervention effect. However, if the problem of estimating the intervention effect is formulated in the statistical decision theory framework, estimation with this procedure is not necessarily optimal. In this study, we formulate the problem of estimating the intervention effect for the two cases, the case where the causal diagram is known and the case where it is unknown, in the framework of statistical decision theory and derive the optimal decision method under the Bayesian criterion. We show the effectiveness of the proposed method through numerical simulations.

UR - http://www.scopus.com/inward/record.url?scp=85065192272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065192272&partnerID=8YFLogxK

U2 - 10.1109/CISS.2019.8692816

DO - 10.1109/CISS.2019.8692816

M3 - Conference contribution

T3 - 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019

BT - 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -