curve_ds_eg.tar

	We consider credibility regions computed from a point cloud
	consisting of draws from a posterior that lie on a singular
	manifold that is embedded in a natural Euclidean parameter
	space. Visualization methods are developed to determine the
	amount of curvature of the manifold.  Methods to visualize and
	report credibility regions in the presence of curvature are
	proposed.  The motivating application is MCMC (Markov Chain
	Monte Carlo) applied to a likelihood that is subject to
	overidentified moment equations. A common approach when
	analyzing such data is to map the data to an Euclidean space of
	the same dimension as the manifold, called a chart, with
	distance on the chart equal to geodesic distance on the
	manifold. That approach is adopted here with the difference that
	our chart variables are interpretable.  Among the examples is a
	replication of the classic Hansen and Singleton (1982)
	estimation using their original data and the methods proposed
	here.
	
For Example 7.3, A Simple Demand and Supply Example, provided is all the
code needed to produce Table 2 and Figure 5 of Gallant, A. Ronald
(2022), "Visualization and Inference From a Point Cloud on a Curved,
Singular Manifold," www.aronaldg.org/paper/curve.pdf, from the included
point cloud emitted by npb. See README.txt in directory ds_run.