Modeling for seasonal marked point processes: An analysis of evolving hurricane occurrences

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a nonhomogeneous Poisson process and propose a nonparametric mixture of beta densities to model dynamically evolving temporal Poisson process intensities. Dependence structure is built through a dependent Dirichlet process prior for the seasonally-varying mixing distributions. We extend the nonparametric model to incorporate time-varying marks, resulting in flexible inference for both the seasonal point process intensity and for the conditional mark distribution. The motivating application involves the analysis of hurricane landfalls with reported damages along the U.S. Gulf and Atlantic coasts from 1900 to 2010. We focus on studying the evolution of the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. Our results indicate an increase in the number of hurricane landfall occurrences and a decrease in the median maximum wind speed at the peak of the season. Introducing standardized damage as a mark, such that reported damages are comparable both in time and space, we find that there is no significant rising trend in hurricane damages over time.Comment: Published at http://dx.doi.org/10.1214/14-AOAS796 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning Time-Intensity Profiles of Human Activity using Non-Parametric Bayesian Models

Data sets that characterize human activity over time through collections of timestamped events or counts are of increasing interest in application areas as humancomputer interaction, video surveillance, and Web data analysis. We propose a non-parametric Bayesian framework for modeling collections of such data. In particular, we use a Dirichlet process framework for learning a set of intensity functions corresponding to different categories, which form a basis set for representing individual time-periods (e.g., several days) depending on which categories the time-periods are assigned to. This allows the model to learn in a data-driven fashion what “factors ” are generating the observations on a particular day, including (for example) weekday versus weekend effects or day-specific effects corresponding to unique (single-day) occurrences of unusual behavior, sharing information where appropriate to obtain improved estimates of the behavior associated with each category. Applications to real–world data sets of count data involving both vehicles and people are used to illustrate the technique.

Étude d'un modèle génératif pour l'analyse en temps réel de trajectoires bidimensionnelles bruitées

Les règles du jeu -- Mise en situation -- Où se situe l'intérêt? -- Pourquoi limiter l'analyse aux trajectoires bidimensionnelles? -- Qu'est-ce que le modèle d'acitivité? -- Pourquoi les modèles graphiques probabilistes? -- Le problématique et les objectifs -- Une approche non supervisée -- Pourquoi Robocup? -- La plateforme de travail -- L'avant-match -- Point de vue de la planification -- Point de vue des modèles comportementaux et d'activité -- Dans le cadre des compétitions de soccer multi-agent -- La formation de l'équipe -- La première approche considérée -- L'alternative gagnante -- Les distinctions du modèle envisagé -- L'échauffement -- Modèle d'activité multi-résolution -- L'espace des primitives -- Le modèle graphique probabiliste (PGM) -- Le modèle de segmentation en-ligne -- Le plan de match -- Les trois contextes d'application -- Méthodologie de test : PGM seul -- Méthodologie de test : PGM avec modèle de segmentation en-ligne -- Validation du PGM- -- Validation du modèle de segmentation en-ligne -- Validation du PGM avec modèle de segmentation en-ligne -- Les échos de vestiaires -- Les principales contributions -- Le rendement et les limites du PGM -- Le rendement et les limites du modèle de segmentation en-ligne -- Avenues potentielles pour le modèle d'activité

Deciphering activity patterns using time-geography framework: A case study of Oklahoma State University, Stillwater Campus

Human societies are organized around activities. Every individual participates in certain activities at all times, which are organized in both time and space. Therefore to understand how human societies are organized, it is important to understand how human activities are organized. Traditionally, methods of activity analysis have employed transportation planning, structural equation, simulation and other computational models. Most of these models use trips and trip making as the bases for activity analysis. Current practice however recognizes activities as the focus of activity analysis since trips are derived from the demand of people to participate in activities. This and other shortcomings of the traditional models have resulted in the search for new perspectives and tools to analyze activity patterns. Hagerstrand's time-geography presents an elegant framework to study and understand activity patterns through several important and clearly defined concepts such as stations, space-time paths, space-time prisms, and activity constraints. One of the most important attribute of this framework is its capacity to capture and represent the sequence of human activities in simple but effective ways. The space-time path is a three-dimensional (3D) trajectory that represents the locations of human activities in a two-dimensional (2D) plane and captures the time and sequence of activity participation through the third dimension - time. Activity constraints also provide an understanding of the necessary conditions needed for human activity to take place. Unfortunately, only a few studies have developed methods of activity analysis using this framework. This study adopts the time-geography framework and concepts to develop two new methods to decipher activity patterns. The daily activity schedule fragmentation index (DASFI) examines the propensity of individuals to organize their activities in chains or fragments. The daily activity intensity similarity index (DAISI) measures the degree of similarity between the activity profiles of people. Both indices can be used in cluster analysis to derive clusters which group individuals with similar characteristics in their activity patterns. A case study with the population at Oklahoma State University - Stillwater Campus proves useful in understanding how people organize their activities and could help in planning geographical space to meet the activity needs of people