Numerical Integration# Economics - 经济
J*Y
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In Bayesian econometrics, we need estimate the moments of functions of
interests, for example, the expecttation of f(a): E[f(a)|D], where
a is a random number and D is observed data.
E[f(a)|D]=Integrate[(f(a)*p(a|d)),{a}]. Where p(a|D) is posterior
density of a. Generally, we can not find
the closed form of the integration, so some numeriacl methods is neccessary.
The first method is Laplace's method. This method changes the problem
to a numerical derivative, which is much easier. However, this
interests, for example, the expecttation of f(a): E[f(a)|D], where
a is a random number and D is observed data.
E[f(a)|D]=Integrate[(f(a)*p(a|d)),{a}]. Where p(a|D) is posterior
density of a. Generally, we can not find
the closed form of the integration, so some numeriacl methods is neccessary.
The first method is Laplace's method. This method changes the problem
to a numerical derivative, which is much easier. However, this