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).
- 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) + ...
- = E[ h(μ)
- which may come in useful for approximating Fisher information, etc. (--DS).