Unsupervised marine vessel trajectory prediction using LSTM network and wild bootstrapping techniques

Increasing intensity in maritime traffic pushes the requirement in better preventionoriented incident management system. Observed regularities in data could help to predict vessel movement from previous vessels trajectory data and make further movement predictions under specific traffic and weather conditions. However, the task is burden by the fact that the vessels behave differently in different geographical sea regions, sea ports, and their trajectories depends on the vessel type as well. The model must learn spatio-temporal patterns representing vessel trajectories and should capture vessel’s position relation to both space and time. The authors of the paper proposes new unsupervised trajectory prediction with prediction regions at arbitrary probabilities using two methods: LSTM prediction region learning and wild bootstrapping. Results depict that both the autoencoder-based and wild bootstrapping region prediction algorithms can predict vessel trajectory and be applied for abnormal marine traffic detection by evaluating obtained prediction region in an unsupervised manner with desired prediction probability.

Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets

Missing data reconstruction is a critical step in the analysis and mining of spatio-temporal data. However, few studies comprehensively consider missing data patterns, sample selection and spatio-temporal relationships. To take into account the uncertainty in the point forecast, some prediction intervals may be of interest. In particular, for (possibly long) missing sequences of consecutive time points, joint prediction regions are desirable. In this paper we propose a bootstrap resampling scheme to construct joint prediction regions that approximately contain missing paths of a time components in a spatio-temporal framework, with global probability $$1-\alpha $$ 1 - α . In many applications, considering the coverage of the whole missing sample-path might appear too restrictive. To perceive more informative inference, we also derive smaller joint prediction regions that only contain all elements of missing paths up to a small number k of them with probability $$1-\alpha $$ 1 - α . A simulation experiment is performed to validate the empirical performance of the proposed joint bootstrap prediction and to compare it with some alternative procedures based on a simple nominal coverage correction, loosely inspired by the Bonferroni approach, which are expected to work well standard scenarios.

Distribution-Independent Empirical Modeling of Particle Size Distributions—Coarse-Shredding of Mixed Commercial Waste

Particle size distributions (PSDs) belong to the most critical properties of particulate materials. They influence process behavior and product qualities. Standard methods for describing them are either too detailed for straightforward interpretation (i.e., lists of individual particles), hide too much information (summary values), or are distribution-dependent, limiting their applicability to distributions produced by a small number of processes. In this work the distribution-independent approach of modeling isometric log-ratio-transformed shares of an arbitrary number of discrete particle size classes is presented. It allows using standard empirical modeling techniques, and the mathematically proper calculation of confidence and prediction regions. The method is demonstrated on coarse-shredding of mixed commercial waste from Styria in Austria, resulting in a significant model for the influence of shredding parameters on produced particle sizes (with classes: > 80 mm, 30–80 mm, 0–30 mm). It identifies the cutting tool geometry as significant, with a p-value < 10–5, while evaluating the gap width and shaft rotation speed as non-significant. In conclusion, the results question typically chosen operation parameters in practice, and the applied method has proven to be valuable addition to the mathematical toolbox of process engineers.

Prediction Regions for Poisson and Over-Dispersed Poisson Regression Models with Applications in Forecasting the Number of Deaths during the COVID-19 Pandemic

Motivated by the Coronavirus Disease (COVID-19) pandemic, which is due to the SARS-CoV-2 virus, and the important problem of forecasting the number of daily deaths and the number of cumulative deaths, this paper examines the construction of prediction regions or intervals under the no-covariate or intercept-only Poisson model, the Poisson regression model, and a new over-dispersed Poisson regression model. These models are useful for settings with events of interest that are rare. For the no-covariate Poisson and the Poisson regression model, several prediction regions are developed and their performances are compared through simulation studies. The methods are applied to the problem of forecasting the number of daily deaths and the number of cumulative deaths in the United States (US) due to COVID-19. To examine their predictive accuracy in light of what actually happened, daily deaths data until May 15, 2020 were used to forecast cumulative deaths by June 1, 2020. It was observed that there is over-dispersion in the observed data relative to the Poisson regression model. A novel over-dispersed Poisson regression model is therefore proposed. This new model, which is distinct from the negative binomial regression (NBR) model, builds on frailty ideas in Survival Analysis and over-dispersion is quantified through an additional parameter. It has the flavor of a discrete measurement error model and with a viable physical interpretation in contrast to the NBR model. The Poisson regression model is a hidden model in this over-dispersed Poisson regression model, obtained as a limiting case when the over-dispersion parameter increases to infinity. A prediction region for the cumulative number of US deaths due to COVID-19 by October 1, 2020, given the data until September 1, 2020, is presented. Realized daily and cumulative deaths values from September 1st until September 25th are compared to the prediction region limits. Finally, the paper discusses limitations of the proposed procedures and mentions open research problems. It also pinpoints dangers and pitfalls when forecasting on a long horizon, especially during a pandemic where events, both foreseen and unforeseen, could impact point predictions and prediction regions.

Nonparametric hyperrectangular tolerance and prediction regions for setting multivariate reference regions in laboratory medicine

Reference regions are widely used in clinical chemistry and laboratory medicine to interpret the results of biochemical or physiological tests of patients. There are well-established methods in the literature for reference limits for univariate measurements; however, limited methods are available for the construction of multivariate reference regions, since traditional multivariate statistical regions (e.g. confidence, prediction, and tolerance regions) are not constructed based on a hyperrectangular geometry. The present work addresses this problem by developing multivariate hyperrectangular nonparametric tolerance regions for setting the reference regions. The approach utilizes statistical data depth to determine which points to trim and then the extremes of the trimmed dataset are used as the faces of the hyperrectangular region. Also presented is a strategy for determining the number of points to trim based on previously established asymptotic results. An extensive coverage study shows the favorable performance of the proposed procedure for moderate to large sample sizes. The procedure is applied to obtain reference regions for addressing two important clinical problems: (1) assessing kidney function in adolescents and (2) characterizing insulin-like growth factor concentrations in the serum of adults.