Monte Carlo tree search (MCTS) has been widely adopted in various game and planning problems. It can efficiently explore a search space with guided random sampling. In statistics, vine copulas are flexible multivariate dependence models that adopt vine structures, which are based on a hierarchy of trees to express conditional dependence, and bivariate copulas on the edges of the trees. The vine structure learning problem has been challenging due to the large search space. To tackle this problem, we propose a novel approach to learning vine structures using MCTS. The proposed method has significantly better performance over the existing methods under various experimental setups.

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There are many software reliability models that are based on the times of occurrences of errors in the debugging of software. It is shown that it is possible to do asymptotic likelihood inference for software reliability models based on order statistics or nonhomogeneous Poisson processes, with asymptotic confidence levels for interval estimates of parameters. In particular, interval estimates from these models are obtained for the conditional failure rate of the software, given the data from the debugging process. The data can be grouped or ungrouped. For someone making a decision about when to market software, the conditional failure rate is an important parameter. The use of interval estimates is demonstrated for two data sets that have appeared in the literature.>