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The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in d ≥ 2 dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on ℤ d with parameter p ∈ (0,1]. For each occupied site v, and for each of the 2d possible coordinate directions, declare the entire line segment from v to the next occupied site in the given direction to be either blue or not blue according to a given stochastic rule. In the ‘one-choice model’, each occupied site declares one of its 2d incident segments to be blue. In the ‘independent model’, the states of different line segments are independent. [ABSTRACT FROM AUTHOR]

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We propose a method for estimating the parameters of contingency table models, which is motivated by a geometrical idea. Our method--bisector regression for contingency tables (BRCT)--is based on a nested structure of contingency table models. Our method estimates parameters corresponding to the interactions of lower orders after estimating or eliminating those of higher orders. BRCTgenerates a sequence of parameter estimates, each element of which represents a model and a parameter estimate. The length of the sequence is equal to the number of parameters, which is much smaller than the total number of models. We describe the BRCTalgorithm and show an example. We provide explanations for two cases: (a) two factors and (b) K factors. [ABSTRACT FROM AUTHOR]

We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, decisions regarding which cargo containers to inspect should be made in real time, and the models used should be able to focus efforts when the risk is higher. In this study, we propose a dynamic approach that treats the data as a time series in order to detect periods of high risk. A regulatory organization will respond differently to evidence of systematic problems than evidence of random problems, so testing for serial correlation is of major interest. We compare three models that account for various degrees of serial dependence within the data. First is the independence model where the prediction of the arrival of a risky shipment is made solely on the basis of contextual information. We also consider a Markov chain that allows dependence between successive observations, and a hidden Markov model that allows further dependence on past data. The predictive performance of the models is then evaluated using ROC and leakage curves. We illustrate this methodology on two sets of real inspection data. [ABSTRACT FROM AUTHOR]