Identifying Water Network Anomalies Using Multi Parameters Random Walk: Theory and Practice

A noise pattern analysis is used to demonstrate how water quality events can be classified. The algorithm presented mimics a random walk process in order to measure the level and type of noise in the water quality data. The resulting curve is analyzed and four different cases are identified. i.e. sensor problem, water source change, operational change and contamination. For each problem, the algorithm identifies a different pattern. This pattern can be used later to reduce the level of false alarms in the monitoring system

Consistent distribution-free KK-sample and independence tests for univariate random variables

A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the optimal partition size is data dependent. While for detecting simple relationships coarse partitions may be best, for detecting complex relationships a great gain in power can be achieved by considering finer partitions. We suggest novel consistent distribution-free tests that are based on summation or maximization aggregation of scores over all partitions of a fixed size. We show that our test statistics based on summation can serve as good estimators of the mutual information. Moreover, we suggest regularized tests that aggregate over all partition sizes, and prove those are consistent too. We provide polynomial-time algorithms, which are critical for computing the suggested test statistics efficiently. We show that the power of the regularized tests is excellent compared to existing tests, and almost as powerful as the tests based on the optimal (yet unknown in practice) partition size, in simulations as well as on a real data example.Comment: arXiv admin note: substantial text overlap with arXiv:1308.155