Parameter transformation for Nested Sampling

[chonlei]

Making a separate issue for using Transformation class in Nested Sampling, as mentioned in PR #1165:

Because we cannot sample from the transformed prior; we can sample only from the original prior and then transform the samples.

The evidence Z = \int L(x) p(x) dx, where L(.) is the likelihood, p(.) is the prior, and x is the model parameter. If we apply a transformation of y = g(x), then Z = \int L(x(y)) p(x(y)) (dx/dy) dy.

My understanding of nested sampling, from a quick read here, we need to first sample from the prior. But we when do the transformation, we can no longer sample parameters y from the transformed prior p(y)dy = p(x(y)) (dx/dy) dy (and then calculate the likelihood with L(x(y))). What we can do is sample y from the original prior p(x(y))dy, and the calculate the transformed likelihood L(y) = L(x(y)) dx/dy...

So that we can merge that PR and close #1070 first.

@ben18785 @martinjrobins @MichaelClerx comments/thoughts welcome!