We investigate state-space abstraction methods for computing approximate probabilities with Bayesian networks. These methods approximate Bayesian networks by aggregating the states of variables. We implement an iterative approximation procedure based on this idea, and the procedure demonstrates the desirable anytime property in experiments. Further theoretical analysis reveals special propertie...

One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric...