Stats

Stein's Lemma:

E[ g(x) * (x-μ) ] = E[ g'(x) ]

where g(x) is an everywhere differentiable function of x, and μ is a location parameter (--Daniel).

 

If h is a "smooth" function of x, and E[X]=μ & variance[X]=ν, the expectation

E[ h(x) ]

= E[ h(μ) + (x-μ) . h'(μ) + (x-μ)²/2 . h''(μ) + ... ]   --by Taylor expansion about μ

= h(μ) + (^ν/₂)h''(μ) + ...

which may come in useful for approximating Fisher information, etc. (--DS).