The Essential Ideas Let us begin by congratulating Danaher and Smith (2011) on an excellent contribution that serves as a lucid introduction to copula modeling, as well as providing a sensible Bayesian approach for its application to both continuous and discrete data. The essential concept we take away is that modeling dependence in multivariate data is facilitated by transforming the marginal ...

The Essential Ideas Let us begin by congratulating Danaher and Smith (2011) on an excellent contribution that serves as a lucid introduction to copula modeling, as well as providing a sensible Bayesian approach for its application to both continuous and discrete data. The essential concept we take away is that modeling dependence in multivariate data is facilitated by transforming the marginal ...

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson distributed, and the probability of no isolated nodes is equal to the probability the ...

Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial B...

We derive uniform and non–uniform error bounds in the normal approximation under a general dependence assumption. Our method is tailor made for dynamic time series models employed in the econometric literature but it is also applicable for many other dependent processes. Neither stationarity nor any smoothness conditions of the underlying distributions are required. If the introduced weak depen...

We construct a stationary ergodic process X1,X2, . . . such that each Xt has the uniform distribution on the unit square and the length Ln of the shortest path through the points X1,X2, . . . ,Xn is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton, and Hammersley [Proc. Cambridge Philos. Soc. 55 (1959) 299–327] theorem does not extend f...