There is a shortage of mobility datasets - real or synthetic - available in the literature, limiting the development of new research. This generates demand for newer large-scale datasets, considering time, space, and population size. This work introduces a novel, two-step approach to generating large-scale mobility data considering the surrounding context, such as traffic. We validate our approach using two real mobility datasets, resulting in an enriched, large-scale dataset with more than 1 million origin-destination trips, which we share with the community to enable new research opportunities.

A typical problem in spatial data analysis is regionalization or spatially constrained clustering, which consists of aggregating small geographical areas into larger regions. A major challenge when partitioning a map is the huge number of possible partitions that compose the search space. This is compounded if we are partitioning spatio-temporal data rather than purely spatial data. We introduce a spatio-temporal product partition model that deals with the regionalization problem in a probabilistic way. Random spanning trees are used as a tool to tackle the problem of searching the space of possible partitions making feasible this exploration. Based on this framework, we propose an efficient Gibbs sampler algorithm to sample from the posterior distribution of the parameters, specially the random partition. The proposed Gibbs sampler scheme carries out a random walk on the space of the spanning trees and the partitions induced by deleting tree edges. In the purely spatial situation, we compare our proposed model with other state-of-art regionalization techniques to partition maps using simulated and real social and health data. To illustrate how the temporal component is handled by the algorithm and to show how the spatial clusters vary along the time we presented an application using human development index data. The analysis shows that our proposed model is better than state-of-art alternatives. Another appealing feature of the method is that the prior distribution for the partition is interpretable with a trivial coin flipping mechanism allowing its easy elicitation.

We introduce flexible classes of linear degradation models that accommodate skewness and heavy tailed behaviors. That is achieved by assuming that the degradation or the reciprocal degradation rates have distributions in both families, the scale mixture of skew-normal and the log-scale mixture of skew-normal. We prove that the distributions for the failure time and the degradation rate belong to the same family for the majority under the proposed models. Such a result is mainly useful to infer about the failure time when the analytical method is considered. To assess the reliability of the system, we consider the posterior predictive distribution for the failure time. We introduce an algorithm to sample from the posterior distribution, which is based on data augmentation technique. We carry out a simulation study comparing the proposed approach with Hamada's method. We analyze data of train wheels degradation that present several atypical paths. Results show that the proposed models performed better than the existent models to analyze datasets which present atypical paths and are comparable to the Weibull model when analyzing light-tailed and symmetric data.

When performing analysis of spatial data, there is often the need to aggregate geographical areas into larger regions, a process called regionalization or spatially constrained clustering. These algorithms assume that the items to be clustered are non-stochastic, an assumption not held in many applications. In this work, we present a new probabilistic regionalization algorithm that allows spatially varying random variables as features. Hence, an area highly different from its neighbors can still be considered a member of their cluster if it has a large variance. Our proposal is based on a Bayesian generative spatial product partition model. We build an effective Markov Chain Monte Carlo algorithm to carry out a random walk on the space of all trees and their induced spatial partitions by edges' deletion. We evaluate our algorithm using synthetic data and with one problem of municipalities regionalization based on cancer incidence rates. We are able to better accommodate the natural variation of the data and to diminish the effect of outliers, producing better results than state-of-art approaches.