We consider the network analytics problem of comparing two distance metrics on the same set of n entities. The classical solution to this problem is the Mantel test, which uses permutation testing to accept or reject the null hypothesis that there is “no relationship between the two metrics.” Its computational complexity is n2 times the number of permutations (based on a user supplied parameter). This work makes two contributions: (1) DIMECOSTP, a more efficient hypothesis test based on uniform random spanning trees whose complexity is n times the number of permutations. (2) DIMECOSTCC, which uses the correlation coefficient between the two sets of edge weights in a random spanning tree as an indication of the strength of the relationship between the two distance metrics. Both methods utilize sound statistical principles. Experimental results confirm the efficacy of our methods.

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For implementing an intelligent urban management, it is necessary and inevitable to know the population size in different areas of Tehran city and identify how they change over time. Population and housing census data can determine the spatio-temporal distribution of the people and how it evolves. However, census will not be implemented across the country in 2021, like a previous manner, due to issues related to the coronavirus pandemic and its prevalence. From this perspective, the prediction of the population size is significant in different regions of Tehran for the year 2021. This paper focuses on developing a statistical learning model for predicting the population growth rate of Tehran urban areas. To be more specific, since the growth rates data are spatially correlated, skewed to the right, and positive, a Birnbaum- Saunders Markov random field (BSMRF) is proposed. We adopt a Bayesian framework for the parameter estimation and spatial prediction and use Markov chain Monte Carlo methods to sample from the posterior distribution. Then, the results are compared with the traditional models.

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