Graduate Seminar: Alexander Murph
Generalized Fiducial Inference on Differentiable Manifolds
I’ll discuss the problem of defining a general fiducial density on an implicitly defined differentiable manifold and introduce our recent solution. Our proposed density extends the usual generalized fiducial distribution (GFD) by projecting the Jacobian differential onto the space that only allows directions of change that satisfy some constraint function. This calculation is shown to be simple to compute and exists under minor smoothness assumptions. To circumvent the need for an intractable marginal integral calculation, we use two different constrained Monte Carlo algorithms that can efficiently explore a constrained parameter space. Then, we consider several simple examples for which a direct parameterization exists and compare our density against these direct solutions.
This is a joint project with Jan Hannig and Jon Williams. In addition to discussing our recent work on this specific problem, I’ll talk a bit about the general ideas of Hamiltonian Monte Carlo and Generalized Fiducial Inference.