Local Conditional Distributions Research Articles

Time reversal and stationarity of infinite-dimensional Markov birth-and-death processes

By using stochastic calculus for pure jump martingales, we study a class of infinite-dimensional birth-and-death processes. A technique, based on a relative entropy condition, which is adopted from diffusion process theory, enables us to also handle the corresponding processes obtained by reversing the direction of time. The duality between the processes of forward and backward time, respectively, is considered for Markov processes, defined by a prescribed family of upward and downward jump rates. A new characterization is obtained of the probability measures, which are invariant for the stochastic evolution associated with a specific set of jump rates. It leads to the conclusion that, if phase transition occurs, then all measures, with a given set of local conditional distributions in common, are invariant provided one of them is.

Distributed estimation algorithms for nonlinear systems

In this paper, we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information. Sufficient statistics for the local distributions are communicated to a coordinator, who attempts to reconstruct the global centralized distribution using only the communicated statistics. We obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution. The results can be applied in designing distributed hypothesis-testing algorithms for event-driven systems.

Non reversible stationary measures for infinite interacting particle systems

Two results concerning the local conditional distributions of a stationary measure for a spin flip process with strictly positive and continuous rates are obtained: 1) The local conditional distributions and the rates of the reversed process determine each other. 2) Either all shift invariant stationary measures are Gibbs with the same potential or no shift invariant stationary Gibbs measure exist.

The lognormal approach to predicting local distributions of selective mining unit grades

When planning highly selective mining operations, the challenge is to estimate mineable ore reserves that will be selected at the mining stage. From exploration data it is not possible to estimate accurately the grade (or thickness) of each future selective mining unit; however, it is possible to estimate the local distributions of these mining unit grades within large panels suitable for long-range mine planning. Application of a cut-off then allows estimation of the recovered ore tonnage and grade within each such panel. Derivation of local conditional distributions is rather simple when the grade is either normally or lognormally distributed. The geologically important lognormal case is fully described both in the stationary and the nonstationary case. Cross validations of these techniques using the exploration data of the Imouraren uranium deposit are presented.

Poisson point processes with exclusion

We give the definition of Poisson point processes with exclusion by their local conditional distributions, treat the existence and uniqueness problem and their applications in percolation theory.