To protect confidentiality, statistical agencies typically alter data before releasing them to the public. Ideally, although generally not done, the agency also provides a way for secondary data analysts to assess the quality of inferences obtained with the released data. Quality measures can...

Given i.i.d. point processes N1, N2,..., let the observations be p-thinnings N'1, N'2,..., where p is a function from the underlying space E (a compact metric space) to [0, 1], whose interpretation is that a point of Ni at x is retained with probability p(x) and deleted with probability 1-p(x)....

Laws of large numbers, central limit theorems, and laws of the iterated logarithm are obtained for discrete and continuous time Markov processes whose state space is a set of measures. These results apply to each measure-valued stochastic process itself and not simply to its real-valued functionals.

Let (E, ) be a measurable space and let [eta] be a probability measure on . Denote by I([eta]) the set of Markov kernels P over (E, ) for which [eta] is an invariant measure: [eta] = [eta]P. We characterize the extreme points of I([eta]) in this paper. When E is a finite set, I([eta]) is a...

Let N be an observable Cox process on a locally compact space E directed by an unobservable random measure M. Techniques are presented for estimation of M, using the observations of N to calculate conditional expectations of the form E [M]A], where A is the [sigma]-algebra generated by the...