Student-t weight parameters

Classes
class	Qgrp
	Standard Student- \(t\) weights. More...
class	QgrpPEX
	Student- \(t\) weights for PEX. More...

Detailed Description

A popular way to build a Gibbs sampler for a Student- \(t\) model [dyk01] [gelman04] is to treat it like mixture of Gaussians, with the covariance of each data point weighted proportionally to its distabce from the mean. The weights are modeled as \(\chi^2_{\nu}\) scalars, with the degrees of freedom \(\nu\) equal to the Student- \(t\) degrees of freedom. It is possible to further construct Metropolis updating steps for the degrees of freedom, but in our experience it complicates computation without adding much to inference. We therefore leave degrees of freedom as constant, to be varied manually by the user. We encourage trying a few degree of freedom values to see how the values affect inference. All constructors for these classes intitialize all weights deterministically to 1.0. Empirically, this seems the most numerically stable approach, and still results in reasonably well-spread starting points as long the location parameters and inverse-covariances are initiated stochastically.