I'm not referring to this normal type of "scaling", I'm referring to raising the whole distribution to a power 1/T which effectively "broadens" the distribution. In the case of a Gaussian, the effect is indeed simply to increase the variance. The reason I want to do this is to increase...
I've hit a problem trying to sample an inverse gamma distribution, 'scaled' using a temperature variable, T. If my distribution is defined as (where the normalising constant k=(b^a)/Gamma(a) ):
IG(x|a,b) = k * x^(-a-1) * exp(-b/x)
then the scaled version is
(IG(x|a,b))^(1/T) = k^(1/T) *...