  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.
